Due diligence refers to the level of effort someone must make in order to have fulfilled their legal duties in a particular situation.
It is the standard of care that person must exercise. In the copyright context, the term is most often encountered with respect to the necessary efforts a would-be user of content must make to locate the holder of the rights in a particular piece of content. This has become an important concept recently with respect to so-called ”orphan works” and the Google Book Search project.