A normal map in games is applied as a SHADER, not a regular TEXTURE. The normal map itself is an image but it is applied as a shader. This is very important to realize. There is no "baking" of the normal map into the object in game.
Every vertex drawn in a 3d program has a normal, which is the way the vertex is "pointing." Every triangle drawn has 3 points, aka 3 verticies. If all the normals are pointing the SAME WAY, let's say they're all perpendicular from the triangle, it will be flat shaded. This is why when you see something with the "normals flipped" it looks almost inside out, because the program is pointing all the triangles / normals the wrong direction.
Have you ever seen a sphere which looks blocky versus one that looks smooth? Take these two examples:
Flat shading, bad normals
Smooth shading, good normals
Technically that last one is phong shading, but don't worry about that. Those two spheres have IDENTICAL geometry and textures, but one looks better. The normals for the flat sphere are all pointing straight out from each face. (It may help to imagine a "normal" as an arrow pointing straight up from each corner of the triangle) The normals for the smooth sphere are all angled slightly away from the triangle face, so there is a perceived smoothness in the shading. Put another way, on the bad sphere, where every triangle meets another, the normals aren't pointing in exactly the same direction so there's a clear visual difference in shading. On the smooth sphere the normals at meeting points all point in the same direction, so the same shading / light calculation is applied to that area.
Now back to a normal map. All a normal map does is tell the program how to shade your object, where the perceived areas of highlight and detail are. Just like you can trick the computer into drawing a smooth sphere, you can trick it into drawing veins, scars, little hairs, or any kind of detail that would otherwise be too fine to display on a game model.
Gaurenteed all modern indsutry games use normal map shaders (amongst many others) on their models because it adds a huge amount of detail without much of a performance decrease. Doom 3 was one of the games that did this very well, using extremely detailed normal maps to make very simple models look very complex. It wasn't the first, but it did it well. Since then normal mapping has become an integral part of model design.
Hopefully that all makes sense and helps you get started in the right direction.