It'll print the reverse of a string, but it will also print everything before it until it hits a null byte. I'd add
<[-]
to the beginning to null out the preceding byte and hope it wasn't important.
As silly as brainfuck seems, I could see something like it being used in nanobots (should such a thing ever come to pass), where memory would be at a severe premium.
Brainfuck doesn't really save more memory than any other Turing machine language. However, it could save you silicon space in your hypothetical nanobot because everything is an increment -- incrementing can be done by a chain of half adders, which require fewer gates than full adders.
>,[[>,]]<[.<]
edit: of course it should be
>,[>,]<[.<]