You can send bitcoins directly to a person's account without going through an intermediary, such as Paypal or a bank. This means that it would potentially be cheaper, but more importantly it would be easier to automate, and easier to start up interesting financial web apps.
I can already do free transfers to anyone's bank account: it's called BACS, every UK bank account supports sending and receiving BACS transfers, the vast majority through a web interface. Takes 3 days, but who cares?
You can do it faster if you're willing to pay a fee, whether that's to Paypal, or to do a CHAPS transfer. If the point is avoiding paying to move cash around, it's already perfectly do-able.
I'd imagine there's more scope for competition. Setting up a new credit card takes a lot of money, whilst exchanging dollars for bitcoins is essentially free (so long as you have enough bitcoins).
That said, I don't think this is the most interesting part of bitcoins.
