CoFHLib, also known as the CoFH Common Library, is a libary that allows Team CoFH and other modders to develop their mods more easily. CoFHLib provides a lot of the 'boring' yet essential code for creating mods. It is not actually a Forge mod in itself.
CoFHLib also contains the CoFH API, which can be used to add compatibility with the various Team CoFH mods.
Note: CoFH Core includes CoFHLib in the mod file. As a result, it is not required or useful to install both CoFHLib and CoFH Core.