It's not the easiest thing in the world to put into words but basically it's about slowing the bat/ cue/ racket/ club foot down. For maximum effect when hitting the ball it makes sense that you only want to be slowing down after you've hit the ball. This makes for quite an expansive follow-through as you were still moving at full pace, hopefully, while you were in contact with the ball. A messy follow-through can mean that you had started the slowing-down motion too early, before you'd hit the ball.
Also it takes quite a bit of effort to come to a stop quickly. Far more sensible to allow the momentum to carry on for a little bit after hitting the ball, and slowing down more smoothly. Not only does it look good, it's also more efficient, less stressful on the body, etc. Again, then, because the most natural and sensible slowing-down action of shots should take a fixed amount of time, as much of this time as possible should be after you've hit the ball.
I hope this helps and also that it's accurate. Can't be much else, really. The key thing is to hit the ball cleanly and with as much power or spin or control as possible -- and then the follow-through will give a good impression as to whether or not this was achieved.