SSD stands for Solid State Drive. It takes the place of a hard drive and is faster because it does not have moving platters. SSDs are faster, but they provide less storage as a HDD that can store 3 TB is cheaper than an SSD that can only store 240 GB.
No you don't need a SSD. But if you do a build with an SSD and use the SSD as your boot drive, your boot up time will decrease by at least half.
SSD"s (solid state drive) have no moving parts, think of them as like a big thumbdrive sort of. Because they have no moving parts like the platters and arm a regular mechanical drive has, they are very very fast as compared to the same mechanical drive and theoretically, should outlast a mechanical drive that has moving parts. Transfer speeds are about double generally, and latency is nearly gone. This makes using Windows, or most programs, very snappy, really fast, really. The bad thing, as stated above, is they are smaller in capacity, and expensive. What most budget builders do is buy a smaller SSD, like 60-120GB and install Windows, their antivirus software, maybe Mircosoft Office, and few programs they use constantly on it, and then get a larger mechanical drive for storing all their data, music, videos, pictures and the like on; the things that don't benefit so much from the speed of the SSD. Putting Windows on an SSD like this really makes for a PC that is simply a pleasure to use for even for everyday use, it really does make everything snappy and almost instant. SSD's will eventually make mechanical drives obsolete one day, not real soon, but not that far away either.