The same reason ordinary money: it's a universal commodity that is the measure of value in the buying and selling of other goods.
Cryptocurrencies have several significant advantages. First, she is not afraid of inflation. If the printing press will go crazy and nashtampuyut mad amounts of roubles, it is logical that the money will depreciate. With bitcoin, this situation is excluded: recall that their number is known in advance and limited.
Another plus is decentralizing. There is no single centre from which the management of the system, and hence the workability of this system, force limiting the spread of the currency extremely difficult. The network simply is no single owner, it is controlled by users around the world.
A further benefit is the anonymity. You can monitor your transactions and see how many bitcoins moved from one purse to another, but to determine exactly who is the owner of the wallet, not so easy. A bitcoin account can be opened by any person, you need the proper software and Network access.