Speed in two areas..
Firstly, the one that makes the biggest difference is the speed it takes to access a file, it's practically instant on a SSD. If you're accessing loads of small files at the same time (like when Windows is doing stuff), an SSD will zip through them in no time at all. A hard drive takes ~9ms per file it seeks out, add hundreds of these up and you'll notice the difference between them.
Secondly, the speed that they can read a large file. A typical top of the range hard drive can read a file at 130MB/s (picking this number out of the air), top end SSD's can read at 550MB/s
They generate next to no heat (if any?) and no noise.
The single best upgrade I've done to my PC in about 6 years
What many people do, is have a 60-120GB drive and use that for Windows/Programs, then have a normal hard drive as the second drive and store all user files/music/photos/desktop on there, since they generally don't need the benefit of super fast file access.
It's all covered in this sticky
http://forums.overclockers.co.uk/showthread.php?t=18040306