Think of bitcoins as numbers and proof of what digital ID owns those numbers.
Technology I understand
Imagine you live in a dorm with 25 other students. You and each of the other students are given a notebook. Each notebook has 260 pages and one of the letters, A-Z written on the cover. On each page, the number of that page is written at the top. Each student is given a notebook where ten pages have the letter of one of the notebooks written down.
So if you're student A, your pages 1-10 have A written on the page at the top. Your pages 2-20 have the letter B written at the top of the page, and 3-30 have C and so on so that the last 10 pages have the letter Z at the top. All the notebooks start out the same, but you can trade a page for some service from another student. Say you don't want to take your turn at kitchen duty, so you go to the guy who has the B notebook and you offer him page 1. All the notebooks currently show page 1 has A written on it, so you add ->B to the top of the page 1 in your notebook, so now it shows A->B. The owner of the B notebook also writes A->B at the top of page 1. Then you each go to half of the remaining students and they write in the same thing. Every notebook now agrees that page 1 belongs to the owner of notebook B.
You can do this over and over, trading pages for services and having everyone update their notebooks to keep track of who owns each page.
That's a lot of work to keep track of pages, but if you all agree that there is some value to associate with each page, then you can use the pages and notebooks to keep track of who owns each page.
Now imagine that the notebook owners get tired of tracking ownership by hand, so everybody puts their notebook notes into their smartphone on a spreadsheet. Now instead of going to each student and getting them to update their notebook, you can just send a text and wait for a reply that they've updated their spreadsheet. That's still a lot of trouble, but it's easier than using pen and paper to track who owns each page of the original notebooks.
Some smart kid writes an app that automatically updates the spreadsheet and sends the reply text when it's done. Now every student can trade a page to someone else, and the two parties involved in the trade just text the other students until everybody has a note specifying what has been traded.
Bitcoins are numbers, but this is prettier
Bitcoins are designed to work much like that. Instead of tracking ownership of pages, they track ownership of numbers. Instead of trusting people to update a spreadsheet, there is a log that gets updated and everybody keeps a copy of that log. Instead of waiting on everybody's log to update when a trade is made, the system just depends on most people having an updated log.
Bitcoins depend on math and computers. Math can be used to prove someone has a specific set of numbers without revealing what those numbers are. The same kind of math is used when you visit your banking website. Your computer has a record of a handful of trusted records and the banking website presents mathematical proof that it owns certain secret numbers which your browser checks against the trusted records as matching that banking website.
Bitcoins work the same way, but rather than using a handful of trusted records for each verification, every user has a log and bitcoins move when the majority of users all agree that their logs match. The logs don't just track whole bitcoins though, they are able to track very small fractions of a coin.
Bitcoins have no value in themselves, they only have value if people agree that they have value. Right now (as I type this) if you want to buy or sell a bitcoin, the value of one bitcoin is about $450 according to most people who are willing to buy or sell them.
All you generally need to know are a few things: Your ID that bitcoins can belong to is called a wallet. You can transfer bitcoins, or a single bitcoin or pretty much any fraction of a bitcoin you desire from your wallet to a different wallet.
You'll need to know:
At the time of this article, lets assume a bitcoin is worth $450. If I want to transfer $50 worth of bitcoin to Human Rights Foundation, I go to their page at http://humanrights.foundation/donate/ and see their bitcoin wallet address is: 18fyEQXaZQgCbNoE5Qjs6W7Pnqc9Yp4PQD so I instruct the software that manages my wallet to transfer 0.11111111111 parts of a bitcoin to that address.
With my wallet manager, I can just specify the value in US dollars I want to send and it will select the matching bitcoin amount. It asks me for the address I want to send to, how much I want to send and then confirms I have entered the right information. That's it.
Since bitcoins are really essentially just numbers with special properties, anyone with a computer can task the computer to run one of the programs designed to find those special numbers. The special numbers that are valid bitcoins are limited and increasingly scarce, so as more of them are found it takes longer and longer for a computer to find a new one. You could task your computer with searching for one and find several quickly back when bitcoins were a new concept. Now you could do the same thing but it would take years, maybe many years, for your computer to find one. People have invested a lot into specially designed computers dedicated to searching for new bitcoins. This process of searching for new bitcoins to claim is referred to as mining. For those people lucky enough to have started when bitcoins were a new concept and for those people willing to invest a lot into systems designed for mining, it can be profitable. For the rest of us, the electricity our computer would use would cost far more then the bitcoins it might successfully mine would be worth.
Once you have a wallet with ownership of some bitcoins or parts of bitcoins you can use them to pay for things from people who accept bitcoins as payment or donate to organizations or people with wallets. If the person or organization you want to pay with bitcoins doesn't have a wallet they can use, several organizations are happy to take some part of the value of the transaction in exchange for converting the bitcoins you pay into a payment type accepted by the other party.
I want food, what can I trade for it?
For example, you can buy a Dell computer with bitcoins. You can buy chairs or shoes among many other things from Overstock.com. You can pay for trips from Expedia. Most things you might want to buy or pay for can be purchased with bitcoins.
A number of bitcoin exchange systems exist where you can buy bitcoins for a nominal fee. I recommend Coinbase since they make it easy to purchase bitcoins and they make it easy to spend them as well.
If you're willing to pay for the service, you can even get a debit card from Swift that will allow you to spend money anywhere that takes Visa cards. The merchant takes a payment in US dollars from Visa, Visa gets its money from Swift and Swift takes the value of that transaction from the bitcoins in your Coinbase wallet.
If you're interested in taking bitcoins as payment, all you need to do is provide your Coinbase wallet address as the target for the payment.
With most transactions where you want to move money from one place to another you have to either physically exchange currency or you have to get entities you both trust to do it for you. That's not difficult in practice because using cash to pay for something or using your bank debit card is a common idea.
Bitcoins don't depend on the authority of a bank or the ability to meet in person. With bitcoins you can transfer something valuable to someone you've never met or you can transfer something valuable to someone without the oversight of a bank. That worries some people.
You can guess which people
Banks have been regulated so that consumers can trust them. Your bank (or credit union) is regulated by government agencies who specify how they must conduct themselves and their transactions in ways that ensure they will be able to fulfill their promises. In return for this regulation, financial institutions get certain guarantees from government that translate to a sense of security for their customers and ample opportunity for the financial institutions to make a profit. Part of that regulation isn't just for the benefit of the banks of customers and the banks though, part of it is in the interests of the government. Certain transactions are prohibited, such as with people in countries that the government has decided to punish.
For many people, the option to eliminate the profit taking by banks or to do business without needing government approval is appealing. Convenience is the driving force for most, but for people who want to do transactions that the government might not (or definitely would not) approve of is the strongest appeal. Granted, for the average person the appeal is being able to transfer money to friends, family and local merchants less expensively than through a bank is what makes them choose bitcoins. For people selling drugs, illegal weapons, illegal services or doing business in countries prohibited by law, bitcoins offer anonymity and a way around the law.
The promise of bitcoin is the ability to cut out the middleman's profit taking from your everyday life and to be able to do business with anyone, anywhere on the internet.
The threat of bitcoin is that people will do illegal business that the governments can't stop or successfully regulate.
Don't do it.
Feel free to take advantage of the perks of using bitcoins, but don't trust it to gain value or even stay stable. What you buy for $10 worth of bitcoins today may be $1 worth of bitcoins tomorrow. It might be $20 worth of bitcoins the week after but the value fluctuates more than most national currencies. Feel free to put whatever funds you can afford to lose into purchasing bitcoins, but not more than that.
Can you spare a couple bitcoins? ($900)
If you're using bitcoins to do business that might be illegal, then I advise against it, obviously. With that said, that's probably the most reliable reason people are going to keep using them. When someone wants to buy heroin from a shady dealer, bitcoins offer a way to do that without the worry that the bank is going to be subpoenaed for the record of the transaction. As long as people strongly want to do illegal business, there will be a market for a way to do it (mostly) anonymously. Human nature being what it is, and bitcoins being the biggest player in the field today, I expect bitcoin to live long and prosper.
Finally there are a few people who put money into bitcoin in the hopes it will become ever more profitable. If you're willing to hire people to do the necessary research and can stand to lose a million dollars or two in the hope it might turn into dozens, then more power to you. That's not me, or most of us, but I wish you good luck. On that subject however, I have this to add: When governments fail to protect their currencies, such as happened in Greece and Brazil, then many turn to alternatives like bitcoin. If you believe that governments will continue to mess things up so bad that their currencies values crash, then you might have a reason to believe in the long term survivability of bitcoin.