When referring to screws, 10-24 is one description of the type of screw you are dealing with. More formally, 10-24 tells us the size and also the pitch diameter of the screw. Taken together, these numbers give us the definition of the screw.
We need to have some method of defining what is what in the world of screws. Some agreed list of what to call each different size and type. This is done by ANSI.
The first definition is about the size of the screw. For a 10-24 screw this is 0.19 of an inch as the major diameter and 0.1379 as the minor diameter.
Screw pitch tells us how far away the threads are from each other: how tight the spiral is if you like. For 10-24 screws this is 0.1629 inches.
10-24 refers only to the size of the screw. It does not tell you what the screw is made of. To determine exactly which screw you need, you'll have to know not only the size but the required material. Nylon, brass, chromed and steel are all possibilities.
Different-sized screws are useful for different tasks. So also are screws made from different materials. A plan or list of parts might specify 10-24 as the size but you also need to choose the appropriate material for the material you are using it on. Many hardware stores list materials that are correct for different screw types. If not, ask the store owner or clerk.