the engine of the game is essentially the corse of the program everything runs thru, it is told what level to load, and what player models to use etc. and it will display and interface with the user to allow them to play
what you are prolly hearing is that call of duty was made with the quake 3 engine, as well as RtCW, MoH, Jedi Knight 2, Jedi Academy, and a slew of others
quake 3 engine is bloody old and a load of crap in my opinion, and in order to get it you have to pay big $$ to ID to get a license for it
if you really want to mess with an engine, you will need to know how to program rather well, and also be able to model or know people that can
and good engine that is cheap(about 100 bux) is the
Torque engine(optimized version of the V12[Tribes 2] engine, released by the remants of Dynamix)