a light map is a second texture applied to a surface. So lets say you have a cobblestone ground surround by some buildings. You only want to use a small repeating texture for the cobblestone. Now you want to fake shadows being cast by the buildings. The shadows need to somehow now work with the cobblestone texture you already have. Blender can assign a new uv layout for the ground that will store the lightmap information. Now blender can mix the cobblestone and the shadows using the two uv layouts and display the results. So the ground will be dark where the lightmap had a shadow and normal otherwise.
Yep, most game engines can’t even produce casted shadows, like those from the building on to the ground. New game engines normal can though. The blender GE does shadows based on face orientation. So if a face is pointing towards a light or the face pointing away determines the “illumination” of the face.
And to make the lightmaps the easiest way in blender would likely be to use texture baking.
Not only shadows of static objects, lightmaps are the main tool to create the appearance of natural lighting, especially the diffuse (indirect) light which doesn’t create hard shadows. Realtime GI is just not feasible (yet), and as said the texture maps are often high-resolution and get re-used or tiled several times, whereas a lightmap for diffuse light may have a low resolution but covers the whole geometry…