Keyways are the specific shapes of different key types. Since most common keys work the same way, with several notches of different heights, the keyway is an extra level of security to ensure that not just any key can work in any lock.
Keyways are usually indicated by a letter, such as C, E, F, G, etc. Each brand of lock manufacturer has invented their own set of keyways. When you look at the front of a lock, you can see the shape of the hole which ensures that differently shaped keys won't fit. However, for compatibility, many manufacturers make the same keyways as other brands so that they can be a viable option for lock replacement.
Schlage C-Keyway is one of the most common, and you would likely recognize these keys by the shape of the grip. In fact, look in your pocket. There's a good chance you carry around a Schlage key every day. Often, you can also see the name of the keyway stamped on the key - in this case "C" or "SC" for Schlage C-Keyway.
But the C keyway is just one of the keys in the family. There is a hierarchy of sorts that allows for a wide range of master keying possibilities. In most cases, the master key would need to be the same keyway as each individual lock. But in the case of the L keyway in the chart above, it could function as a master key for most of their other keyways.
Most of the time you don't need to worry about which keyway to order, unless in the case that you need to match an existing building standard. That you would need to check with your building superintendents or facilities managers.
Some special types of keyways are higher security than others, depending on whether they have additional security features or because of the actual lock that they're designed to operate.
Interchangeable cores are available for most of the common keyways.