I tried to follow an explanation of what Bitcoin(s) is/are, but I still don't get it.
If I've followed it correctly . . .
Bitcoins are artificial money (I know, all money is artificial, but hang on) that don't have a physical form. Instead, they're computer-code bits that theoretically can't be copied or forged. They're like valuable World of Warcraft magic items that there aren't a lot of, except they're only valuable because people agree they're valuable, not because they help you kill dragons LOL.
You can buy bitcoins with other money, or you can 'mine' them. The mining process is complicated but involves doing a lot of number crunching. If your mining computer system does enough number crunching, then the Bitcoin Central computer will release a bitcoin to you. The reason it's set up this way is so that you have to
do something to get bitcoins. It takes work to earn them.
Also, there are three other wrinkles meant to enhance the value of bitcoins:
1) There will only ever be so many bitcoins, and then no more. The Bitcoin Central knows how many it's released, and a few decades from now it will stop releasing them, forever. I think the total number that can be released has also been set. So there's a finite supply.
2) As bitcoins get released due to 'mining', the Bitcoin Central makes it harder to mine more bitcoins. It takes more and more number crunching, sort of like a mine where you have to keep digging deeper to find more gold. The easy bitcoins have already all been mined, so a computer rig that could mine them last year can't realistically get any this year.
3) Bitcoins are a currency not controlled by any government. The Federal Reserve doesn't control how much they're worth and can't arbitrarily buy them up (in theory). You can buy stuff with them tax-free (in theory), and it's hard for a government to track their use (in theory).
So they're pretend cybermoney, except they're actually worth something. Honestly, probably the biggest threat to their value is that they may be replaced by some more popular form of cybermoney. Like how MySpace got replaced by Facebook.
Although if people get all hot for Facecoins, it'll just be another nail in our species' coffin.