1. Let’s get in the car and go for a drive. We don’t have to decide before we start where we’re going; let’s just play it by ear.
2. I’m going to watch to see how the situation develops and decide what to do as I go along. I want to play it by ear and see what happens.

Compare to: wing it; by the seat of (one’s) pants. The expression probably originates from the idea of playing a piece of music by ear, i. e. , not reading the music as one plays but simply listening to the piece, picking out the notes by ear and then playing it.