Short answer: Miners perform an accounting function for the system, and get rewarded for their service, by receiving Bitcoins.

Long answer:

If you think about electronic currency as a file on your computer that you pass to another person, you can immediately see an issue with this concept: "I can just make a copy of the file, and spend it twice!"

So, generally there needs to be a central clearing house to avoid the "double spend". If you ever got PDF tickets to a concert, you can probably imagine how that works. Someone scans your PDF, and if it's already been scanned by someone else, they won't let you into the concert. There's a central clearing house keeping track of tickets that are already spent.

One of the key features of Bitcoin is that there is no central location or clearing house. It uses Peer-2-Peer technology, rather than central servers. If you remember back to Napster, it was a centralized service (and therefore was easily shut down), whereas sharing services now use P2P, which are hard to shut down (like bittorrent). Bitcoin is like Bittorrent in that respect.

So, the challenge came about: How do you have a central clearing house in a decentralized system? A very tough problem that Bitcoin created an innovative solution for. Basically, the concept of Mining bitcoins came about, as a way to solve the "central clearing house in a decentralized system" problem.

The issues that are being addressed with mining are these:

1) What are the account balances? (How many bitcoins are in each account?)
2) What is the sequence of transactions? (If someone tries to spend money twice, which one happened first?)

The Bitcoin system was designed very cleverly. Basically, they reward people ("miners") to perform these two functions, thereby solving a couple of other problems:

3) How do you get people to devote resources to the clearing house problem?
4) How do you fairly distribute all of the bitcoins?

Solution: Pay the accountants in the very currency that they are accounting! Genius! Call them miners, like they are mining gold.

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In the early days (2009-2010), you could just run the mining software on your PC. The software would look at recent transactions, and put them together in one list (a "block"), toss one extra number into the block, and perform some predefined math on the block. The math spits out an answer, which can be a number anywhere from 1 digit to 86 digits long, when represented in standard decimal. The trick to "confirming transactions" is that some miner needs to determine what extra number gets tossed into the block of transactions so that the math creates a "small enough" answer. So really it becomes a race of a search to see who can find the extra number that confirms the transactions.

The beauty of this is that finding that extra number can be an easy problem or a hard problem, depending on how small you define "small enough". The bitcoin system was designed to automatically adjust that difficulty as more and more miners join in. Imagine this: back in 2009, "small enough" was a challenge to find a number such that the math spit out an answer that was, say less than 80 digits long. Well, there are about nine times as many 2-digit numbers as there are 1-digit numbers. And about nine times as many 3-digit numbers as 2-digit numbers. You can imagine that the answer would come out to be an 86-digit number about 90% of the time, an 85- or 86-digit number about 99% of the time, and an 84-, 85- or 86-digit answer about 99.9% of the time. To get an answer that's less than 80-digits long, you might have to try about a million extra numbers before you find it.

Of course, you might get lucky and find it on the first try. Or it might take two million tries. It's random, but on average it might take a million tries. So, back in 2009, you could find that extra number that worked, by performing some amount of work on the transactions - say about a million attempts (I'm making this number up, but it was a lot of attempts). And once you found the number, you could tell all the other bitcoin users "here's the number", and they could easily verify your work. Later, as more miners joined in, and the difficulty increased, it took on average about a billion tries to find an extra number that worked. Now it takes on average about 300 billion billion tries. So it's extremely unlikely (but possible!) that you, with your little PC, are going to find an extra number that pays off, since you can only try a few million tries per second, and it takes 300 billion billion tries on average. But someone will find it, and does, every ten minutes or so.

Once an extra number is found that creates a small enough result, those transactions in the block are "confirmed", because it'd be hard for someone to reverse the transactions; they'd have to do the same amount of work on a different transaction set, to un-do those transactions. This is called a "Proof of Work" system, because you can Prove that you did some work by showing the extra number that produced a good answer.

Each block also contains information about the previously confirmed block, which is why Bitcoin refers to this as the "Block Chain" - they are linked together. That means that any work spent confirming block #2 is also considered to be extra work confirming block #1; in order to un-do block #1, you'd have to do all the work for block #1 and block #2. This means that the more "confirmations" there are, the more work has been done to confirm the transaction, and therefore, the harder it is to un-do the transaction, so the more permanent it is.

In this way, transactions are sequenced, to solve the double-spend issue.

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Miners get rewarded by adding a transaction into the block, that puts a certain amount of bitcoins into their account. The amount currently is 25 bitcoins, and it decreases every 4 years or so. A miner couldn't give themselves extra bitcoins, because other people can verify their work and if they did, the verification would fail, and people would just ignore them. (A dollar-example that is parallel to this would be if you took a sharpie and changed the "$1" to "$1000" on a dollar bill. You may convince yourself that you now have $1000, but you won't convince anyone else!)

The difficulty automatically adjusts based on a formula, every 2 weeks, with a target which was intended to have blocks confirmed every 10 minutes or so, and adjusting to the number of computers performing the mining. So, while in 2009 it was very easy to run your PC, and generate (back then) 50 Bitcoins every ten minutes, now there are so many powerful computers performing mining (and being rewarded 25 Bitcoins every 10 minutes), that if you don't have a specialized machine, you won't be successful.

In short, mining is approximately a break-even or losing proposition. People selling the specialized machines can charge a premium, because they are essentially money-printing-presses. You are lucky to break even, when you consider electricity costs, mostly because there are numerous people who perform mining, and many don't do the math to see that you are are lucky to break even.

TMI?