It means 'focused on the task in hand'; this may entail speed, but it is much more than that. The term comes from football, where every player should know where the ball is, who has possession, where it is moving, etc., and every member of the team should know exactly what to do next. This means being very very awake and aware of everything relevant: that is what it means to be on the ball.

"On the ball" doesn't exactly mean "quick." It also means "ready, always able to perform duties effectively." It means "efficient" or "competent." For example, suppose you always need brochures to hand to clients. An assistant who lets them run out "isn't on the ball." An assistant who checks the supply and reorders in time so that they never run out is "on the ball."

Jimmy's explanation is very good. A common saying to players by sports coaches is "Keep your eyes on the ball" with the general meaning of "understand what's going on, understand what you need to do, and do it." Being described as "not on the ball" is a strong criticism.

It doesn't only mean quick to understand, it is more general than that. It means any type of doing something quickly, or getting going. In this case it means get them moving, get them doing something quickly.