1. Mentally perceptive and responsive
   "The new employee is really on the ball, quickly learning all aspects of the job";
   - alert, alive, awake
    
2. (sports) being in control of the ball
   "The midfielder was always on the ball, directing the play"
    
3. [informal] Alert, competent, efficient
   "The new employee is really on the ball"

See also: aware, cognisant [Brit], cognizant

Encyclopedia: On the ball, City