It's a 'Solid State Drive'.
Essentially, it is a faster version of a hard drive. However, it's MUCH more expensive than normal hard drives, but there are also different types of hard drives and the cost (and speed) depends on the RPM (revolutions per minute) of the hard drive. You start putting that sort of stuff into the equation when you deal with desktops ie: WD Caviar vs WD Green vs Velociraptor etc which can get 5400 --> 10k+ theoretical RPM.
Most people who get hard drives tend to partition their primary drive into a 'OS' partition and an "everything else" partition.
So yes, SDD is faster than HD, which is good ofc. However, it's smaller in capacity. This is bad because the smaller capacity means it's a LOT easier for things to get cluttered (fragmented sorta). This can even go to the point of almost 'cancelling' the effect of the SDD so you may as well just get a normal HD for half the price and twice the capacity.
If you want to make the MOST of SDD, you should get the 256GB one. That way, the 'cluttering' isn't an issue anymore and you can take full advantage of the SDD's proper speeds.
If you get a 64GB SDD for OS but have a separate hard drive for everything else, that's fine because the stuff from the hard drive won't affect the SDD.
However your case is different because you only have the one hard drive, so your work, movies, music etc etc WILL get mixed in with the OS and slow it down.