1. To refrain from moving very much or at all. Often said as an imperative. Please, stay still! The longer you keep fidgeting, the longer it'll take to put on this sunblock! You'll need to stay still while the MRI machine is running.
2. To refrain from making very much or any noise. Often said as an imperative. The crowd stayed very still as the golfer began her final putt. I expected the whole classroom to erupt into noise, but to my surprise they all stayed still.