Swap space is what they call Virtual Memory on Windows and Mac.
It's either a file (the Windows way) or a separate partion on your harddisk. The rule is to make it 2 times your RAM (or something near that, but this is must important up to 512 MB RAM).
When your computer runs out of fysical RAM, it copies the contents to SWAP, so it can calculate your new instructions, without losing the data. It speeds up the computer, because you don't have to recalculate everything (or something like that).
Knoppix should work anyway, it is created to not use a harddisk, but it will be slower, if you don't have that much RAM.
Carsten B. Jensen