ssd is fairly expensive right now. Probably like 3to 4 times the cost of a hhd. SSD is basically like a storage you find in your usb or ipod touch. It has no moving parts. HDD has a moving parts so it has to spin the disc inside it to read the data while for ssd, its all right there. SSD, since it has no moving parts, its more durable>>not like HDD, when you drop it, there is a high chance of wiping all your data.
Probably the main advantage of ssd is just the super fast read and write speed, way way way faster than a regular hard drive (HDD). If you install your operating system to the ssd, your computer could boot in 1/2 or 1/3 the time in comparison to the HDD one. When you install a game to ssd, the loading time will be reduced significantly. Take a note that installing any games to an ssd wont give you extra frame per second