They are the pretty things that sit on top of the keyboard. These were the first things I experimented with when I was getting into the hobby. You will notice that the coolest looking keycaps are usually only available via group buy or at exorbitant amounts in the after market.
The two materials generally used for keycaps are ABS (Acrylonitrile Butadiene Styrene) and PBT (Polybutylene Terephthalate). Both the materials have a different feel and sound to them. Switch and click has an awesome piece on what the differences are.
Image via Keycaps.info
The profile of the keycap refers to the overall shape of the keycap. There are certain profiles that have different heights for each row to allow for different key heights. The cherry profile is the most common. When picking a profile it's really down to preference. The keeblog has an in-depth break down of each profile you should checkout.
There are a number of manufacturing methods. They refer to how the legends are printed on the keycap. If you are picking a keycap for a RBB backlit keyboard consider picking up doubleshot or pudding keycaps. They are manufactured in such a way that RGB lighting can shine through.
Links:
Thocstock - For In-stock parts
Mechgroupbuys - They track keyboards group buys