One of my favorite places to explain things is a bus stop. This is usually exactly when someone has just said something along the lines of ‘I suck at math’ and so I feel its necessary to make them doubt that.
New to the list of on the fly analogies for non-math students: Matrices!
Me: Well a matrix is like a spreadsheet; have you ever used excell?
Student: Uh not really…
Me: Hmm Wait! Have you ever played BattleShip?
Me: It’s like that!
Student: Oh! Sink!