It's an instruction set. It extends and in some ways replaces the SIMD instructions added to MMX, like SSE did before it. They allow performing certain operations on multiple pieces of data in fewer clock cycles than it would take to do the same with traditional instructions.
Firefox, and many other applications, now utilize compiler switches (Some of which are the default) to add optimizations to the software to utilize those new instruction sets. It can also be utilized for cryptography which makes it useful for things like SSL.
here is a wiki page describing new instructions added with each x86 Processor.
