Texels are like Pixels. Pictures are made up by different pixels, similar to this, textures are represented by Texels. A texel is the container for the pixels. An example of texel density being used is that a large wall may have a texture map of 1024 x 1024. This may be the center piece object so a smaller box that may be next to the wall may use a 512 x 512 texture map. This is due to the box taking up less space therefore the texture will not need to be as detailed; this also saves file size space.
This can be used to make sure that the textures throughout an object are the same size. This is so that a model does not have an extremely detailed leg but a pixelated body. The leg may fill the same amount of space on the UV map as the Body, this would allow it to have the same texel density.
Below is an example of an objects UV maps, the bad example is showing all of the different meshes within the object having their UVs overlapping in the same map, this problem can be solved by having the different meshes having a different map.
joshforrestnextgen 