To elide something is to omit it or get rid of it. If your parents are especially strict, you might tell them about the A you got on your English essay and elide the fact that you failed your math quiz.
If your school is putting on a production of "Grease" and the director cuts a major scene from the play, you can say she elides it. And when an elected official gives a speech, he's almost sure to elide certain topics that are too controversial or negative. Elide is also used in grammar to describe the way people speak when they leave out certain sounds. It comes from the Latin elidere, "strike out or force out."