To be alert; in command of one's senses.
Some authorities have suggested that 'on the ball' originated in the sporting arena, and alludes to runners being on the balls of their feet, eagerly ready to run a race. This has some similarities with being 'up to scratch', which derives from boxers or runners being ready at the starting line. It is a plausible derivation, but has nothing to recommend it beyond that.
A more commonly advocated location for the source of 'on the ball' is the Royal Observatory at Greenwich. This is where the oldest surviving and best known time-ball is sited. The Greenwich time-ball was installed in 1833 to signal the accurate time to passing ships. It was, and still is, raised just before 1pm each day and falls as 1pm strikes on the observatory's clock. Captains needed to have their ships' chronometers set accurately in order to navigate correctly, hence they needed to be 'on the ball'. It's a nice story and there are any number of tour guides around the observatory who are all too happy to repeat it. Unfortunately...
Need I go on? It isn't true.
The phrase 'on the ball' did actually originate in the sporting arena, but relates to the eyes rather than the feet. It is a contraction of the earlier expression 'keep your eye on the ball', which advice has been given to participants in virtually every known ball game. For the source, we need to look to early ball games. The phrase is recorded in early records of cricket, golf, croquet and baseball and many people regard baseball as the origin. Well, that appears to be almost true - the earliest citation that I can find in print comes from the English game of rounders
See full article at http://www.phrases.org.uk/meanings/on-the-ball.html