I wanted to know what does it mean when people talk about Unreal engin... or Doom engin??? That their games run on those Engin... what exactly is an Engin???

I think you ment Engine. Engine ios just the technology that drives the game. The Unreal Engine is the core software at the heart of UT, UT2003 and other games.

It has a two-tier structure:

1. the C++ code, which in Unreal we call the "native" stuff. This handles all the low-level stuff and platform-specific things. It runs a virtual machine similar to the Java VM, on which runs...
2. the UnrealScript stuff. This is an object-oriented language that looks similar to Java or Javascript.

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yeah gsurface pretty much summed it up...its the core of the game..where graphics are rendered

But is it possible to produce a game without an engine??

I did a battleship 3d with opengl ....
but i don't remember using any engine ... or wasn't aware of using one?

yeah you CAN create games without engines (or using another developers engine) butt....to have any real time graphics rendering game (with great effects) the games usually have complex game engines..that power everything

so engine are use only for graphics??? Does it have anything to do with AI ? Or it's always coded by the programmers?

well lets put it this way, Warcraft 3's engine is the map maker. The users create maps and scenarios from the map maker, but the game itself is run by the engine that you can make do what you want in the map editor. Same thing with Starcraft and Never Winter Nights. Does that make more sence?