Cryptocurrencies are computer generated currencies. They are brought into existence by "mining" which, as its main function, has the purpose of confirming a record of accounts and movements, called the blockchain. Coins are given to successful miners as a reward.

Coins, once generated, are stored in wallets that are password protected. Coins can be sent from one wallet to another. Each transaction gets appended to the blockchain after being verified by the mining activity.

Total number of coins to be generated is generally limited, and the velocity of generation of coins is variable. Generally, it starts out very fast and gets progressively slower towards the end of the pre-programmed stash of coins ever-to-be-issued. 

Coins appreciate in value if there are more requests by buyers than there are offers by sellers.

In the case of Bitcoin, it is assumed that the value of coins will appreciate greatly, as the network expands. More users compete for a similar number of coins means the price of each coin goes up. 

There are different types of currency. Bitcoin is the original and there are now over 200 clones where some of the parameters are changed. Best way to find out about the workings of those is to go to this page

Crypto-Currency Market Capitalizations

where coins are listed according to their "value" or market capitalization, which is calculated as the number of coins in existence times the current price in US$.

Each coin's name links to that specific coin's information where you can dig deeper.