Serials are used by MTA and server administrators to reliably identify a PC that a player is using. They are bound to the software and hardware configuration. Serials are 32 characters long and cointain letters and numbers.
Serials are most used for banning players, because a computer with a dynamic IP can change when the computer requests a new IP, but resources can give them new uses.
Serials are the most accurate form of identifying players that MTA has. However, you shouldn't rely on them entirely: serials may be able to be faked, although this is quite difficult to do, and it's very likely to cause errors to the client that can lead to a global ban if asking for help to fix them. It is also not guaranteed that two players will not have the same serial, but that is extremely unlikely. And finally, a player can simply use another computer with a different serial.