Plain English Meaning
An instrument that tells you two things at once: how fast the aircraft is turning, and whether the turn is being flown smoothly with the right amount of rudder. The little ball at the bottom shows whether the turn is coordinated -- if the ball is centered, the turn is balanced; if it slides to one side, the rudder input is wrong.
Full Definition
Two related gyroscopic flight instruments that show the rate at which the aircraft is turning and whether the turn is coordinated. The turn-and-slip indicator (older design) uses a vertical needle to show the rate of turn around the vertical axis, while the turn coordinator (newer design) uses a small aircraft symbol that banks to show both rate of roll and rate of turn. Both instruments include an -- a curved tube containing a ball in -- which indicates whether the rudder and are properly balanced during the turn.