Delegate lends an official air to passing off your work. If you don't like cleaning the bathroom, you can try to delegate that task to your little brother.
A delegate is also an elected official, or the person who is doing the task you delegated them to do. In presidential primaries in the United States, you do not vote for a candidate, you vote for a delegate whose job it is to vote for that candidate at a convention. Be careful with how you pronounce the end of the word. The elected official is pronounced DE-lə-git whereas delegate as a verb should be DE-lə-gāt.