Decentralized --- It is not controlled by any one government or entity, therefore it is in theory safer and more globally acceptable.
Anonymous --- In theory it can be almost as anonymous as a cash payment.
Less costly --- Since there are no banks controlling it, the overhead is lower. So, for instance, if someone wanted to send money to someone else somewhere in the world, instead of paying large transfer fees (or cash transit fees with something like Western Union), the fee would be very low, almost free.
I am sure there are other reasons that make it superior to traditional fiat systems, but these are a few off the top of my head. There are also downsides that other cryptocurrencies such as Ether (which runs on the Etherium blockchain) attempt to address.