Conventional HDD's contain a disc that spins to load/find your data... For example, when you go to view files in 'My Computer' etc, there is a delay between which the disc HDD's try and find all this data... This is called 'seek time' (i.e. the time it takes for the disc to spin around and find and read all the data.)
Solid State Drives (SSD) eliminate the disc entirely and all your information is stored on microchips... SSDs have a much lower chance of corruption etc, since it doesn't contain any moving parts, it is much more difficult to damage/corrupt etc.
So to sum it up, they are faster than your normal HDD. In my opinion, the average user won't notice much of a difference.