Ok, so hard drives are the current de facto standard storage unit in computers. They use spinning magnetic platters, are generally highly reliable, and failure does not often incur a total loss of data (although, depending on the extent of failure, the data may be costly to recover). Solid state drives use flash based storage that, like a hard drive, is nonvolatile, but unlike a hard drive a solid state drive has no moving parts and therefore is less likely to experience a mechanical failure, but data recovery can be more difficult if not impossible, given the fact that a failure of a flash storage unit would likely render any data on that unit irretrievable. Solid state drives are also a very new, rather untested technology.
Flash storage will hold less than hard drives, on average, and will generally be far more expensive. Also, there are many mixed reviews about the reliability of solid state drives, with many failing after less than a year.
However, solid state drives, or a more technologically advanced form of them, will likely be a future standard due to the fact that they are able to access data MUCH faster than conventional hard drives. With a solid state drive, you WILL notice a substantial increase in start-up speed, data copy rates, etc.