To dignify is to grant nobility or respect to something. Dignifying raises the status of things.
Dignity is a quality of honor and respect, so to dignify is to give greater respect and honor to something or someone. The presence of the President would dignify a military ceremony. Medals are given to dignify soldiers. Treating people with respect and taking them seriously dignifies them. Often, this word is used in a negative sense, as in "I wouldn't dignify him with an answer!" That means the speaker doesn't feel the person asking the question deserves respect.