To play it by ear is to act spontaneously and according to the situation. Playing it by ear means you have no game plan.
The original meaning of this term was to play music without sheet music, meaning you either remembered the music or improvised it. From there, it came to mean other types of making it up as you go along. If a quarterback plays it by ear, he abandons the called play and tries something different. If a politician plays it by ear during a speech, she is making it up on the spot. We all have to play it by ear sometimes.