Hard Disk drives are mechanical. They have a rotating metal disk and have an arm that rides to and fro above the surface of that rotating disk. On the tip of that arm is a 'head' reading magnetically stored data layed out in the form of tracks, sub-divided into sectors.
SSD, Solid State Drives are purely electronic in operation, with no moving parts. Their architecture and functionality varies more than I would like to write about here, but suffice to say that data is handled in a similar way to your computer's memory, except that the data is kept there. SSD's read data at many times the speed of a Hard Disk Drive, but write data at the same speed, however this is changing with much more costlier Drives.
If a Hard Disk Drive fails, there is often a good probability that data on it can be salvaged. A different story regarding Solid State Drives, when they fail then in 99% of the cases everything is lost.
This is just an overview, but if there is anything specific you need to know, please ask.
Hard drives basically have unlimited read/write cycles - as long as they are functional, you can read/write data to them without concern. SSDs have a limited number of read/write cycles - NAND flash that most use has a limit of about 10,000 write cycles, although modern SSD controllers (built into the drive) will wear-level the writes in order to increase performance. Consumer-grade products do this pretty simplistically, so they should not be used for system drives (in my opinion) - best for read-mostly applications. Commercial-grade products apply very advanced mathematical algorithms in order to maximize the life expectancy of the drive, and are apparently very reliable and long-lasting. However, the price differential between consumer-grade and commercial-grade drives is very significant. As the old saying goes, "you get what you pay for"... :-)
Actually the Hard disk drives use a type of magnetism that allows very small "bits" on the disk to either be 'on' or 'off'. In this way, data is encoded in a binary form. HDDs are usually set at either 5400 RPMs or 7200 RPMs or 10000 rpm. This is a reference to how fast data can be accessed off the disk. Solid state drives don't use these "bits", but instead record a type of electrical energy on their surface which allows them to store much more data in a smaller space. Solid state drives also access data much faster, because they don't have an RPM speed.