I'll try to explain Bitcoin.

Imagine a super huge spreadsheet. Each column is an "account number" that is going to keep track of how many coins are in that account. And rows get added on over time, tracking how money moves from one person to another. Initially, there are no rows, because nobody started with any coins.

This spreadsheet can be seen and modified by anyone on the internet. But in order for you to be able to change one of the "account balances", you have to follow a certain set of rules, or everyone else will simply ignore your change. The rules are 1) rows can only be added to the spreadsheet, not removed. 2) you can only submit requests as to what gets added to the next row of the spreadsheet. 3) You can only increase the count in one account if you reduce the number in a different account, and prove that you have the password to that "spending account" column.

Everyone on the internet can see your requested change in the spreadsheet, and can validate that it's a reasonable change - that you aren't creating coins out of thin air, or spending coins that you don't have.

There are two giant hurdles at this point: 1) who gets the coins to start with, and 2) how do you decide which "change requests" get put into the spreadsheet as permanent entries.

And the clever way this is accomplished is that both problems are solved at the same time: The coins are distributed to the very people who are helping to protect the integrity of the spreadsheet, and add rows to it.

People race to try to find a very rare number such that when the number is combined mathematically with the set of Change Requests for the next row, it results in a very tiny number. It's a hard math problem to solve (you can only solve it by trial and error), but an easy math problem to verify ("yup, using that number in the equation creates a really small result.") And the person who finds this number gets to add 25 bitcoins to their "account".

This giant spreadsheet, or ledger, is shared using a peer-to-peer network, with a set of rules and no main person or company in charge. If you try to operate outside the rules, people just ignore you. Much like if you hand-wrote your own $20 bill - you can do it, but people will not accept it.

"coins" are just an abstract concept. Bitcoin holders really just have a sort of "account balance", which they can spend simply by proving ownership (with a sort of password). This is much like your bank account is just a number - and there aren't any real pieces of paper for each number in your account.

The advantages of the system are many: You can personally hold a lot of coins with near zero cost. You can transfer them nearly instantly, nearly free to nearly anyone in the world. And when you own one, you know you own one of a limited supply - there will never be more than 21 Million of them - an arbitrary number that was defined in the rule set.