There are lots of ways to send money - western union, paypal, bank wire, etc that are more established and fairly quick. What are the advantages of using bitcoin from a bitcoin-proponent's point of view?
The primary advantages are:
Speed and price. You can transfer money anywhere in the world within minutes with negligible fees.
No central authority. Bitcoin is not dependent on any company or government to maintain its value.
You can start accepting bitcoins instantaneously, without setting up merchant accounts, buying credit card processing hardware, etc.
Bitcoins are less traceable than many types of monetary transactions (though not anonymous).
Bitcoins cannot be counterfeited and transactions cannot be reversed.
No transaction blocking or account freezing. We have seen governments freeze bank accounts of dissidents and payment processors refuse to process certain types of transactions (wikileaks, online gambling in the US, etc). With bitcoin this is impossible.
A known amount of inflation. Bitcoin is seen as a store of value because the total number of bitcoins that will ever be created is known in advance and it is impossible to create more than that.