An " elevator speech" is a brief and concise statement that describes in 10-20 seconds what your position is, the benefits that will occur if we take this position and the action.
"Evevator" comes from the the idea that you have entered a elevator and meet some one who is very important to the oputcome of your project, the person asks "how things are going?" you want to be in the position to state your business case clearly, concisely and convincingly.