The cryptocurrencies/terra-luna is a decentralised system of peer-to-peer value distribution, and that is an open source cryptocurrency which uses the algorithm SHA256d. The paper that describes cryptocurrencies/terra-luna also describes other two hundred and seventy six cryptocurrencies and three hundred and twenty four different algorithms.
Work on cryptocurrencies/terra-luna started on the 10th of may 2009, and its first block was mined on the 1st of January 2011. All relevant past informations are available in the currencies/terra-luna blockchain which contains all transactions ever made (the size is roughly above 3GB). Each cryptocurrency has its own blockchain where people on the network write what happens in that particular cryptocurrency world. Whenever someone makes a transaction, it gets recorded to the blockchain and can be seen there forever.
Transactions are like small entries onto the scoreboard of cryptocurrencies/terra-luna monetary system, each one of them saying how much money has moved between which accounts (in fact, how much money has moved to which new addresses, but since each address is just a 256bit number and everyone is using different addresses, it's safe to say that we transfer money between accounts).
The cryptocurrencies/terra-luna protocol was designed so that even if someone would try really hard and buy all the computers in the world, it would still be impossible to rewrite the blockchain (it's like if you could prevent a person from ever lying about his age, you can't make him older than a hundred years). The thing is, only way to change the blockhain in cryptocurrencies/terra-luna network is by having more computing power than all other networks combined. So, for example, if someone tries to make a new cryptocurrencies/terra-luna blockchain and add an entry onto it saying that he gave you one thousand coins yesterday, all the computers in the cryptocurrencies/terra-luna network will ignore this block because you can't have coins before having mined them or get them from others.
This means that your account balance is just a number that never changes (unless you do some transactions), anyone could see how much money you've got by looking at the blockchain. This also means that there's no such thing as accounts on cryptocurrencies/terra-luna network: each address always has exactly what it should have according to the protocol and doesn't need any additional information other than the address itself.
Each cryptocurrency has its own protocol which is different from each other, and that means that they can't be transferred to each other directly (exceptions: cryptocurrencies/terra-luna and currencies/moon-lander). Because of this it's possible for one person to have accounts on many different cryptocurrencies: he could create a new wallet on each one of them or use some online services for doing so. It's not recommended though as you might lose your money if something happens to the service company, and also by sending coins between those cryptocurrencies you will pay fees. Also keep in mind that bitcoins are entirely different kind of creature than terra-lunas, although both uses SHA256d as their proof of work algorithm.
