I don't really like the term on the bit, but for simplicities sake I'll go with it.
When a horse is on the bit, it is taking more weight on its hind legs than its front legs. Its hind legs are stepping under its centre of gravity, its back is round and swinging, and there will be a light but consistant contact through the reins to the bit. The horse will have a soft jaw and poll, with its head positioned slightly in front of the vertical.
The most important thing to note, is that this comes ONLY from learning how to ride active hind legs into an elastic hand, to contain the energy from the hind legs and allow it to flow through the horse's body. Essentially, the horse is like a coiled spring when this occurs.
A horse that is above the bit, will usually also have a tight back, and trailing hind legs. Its jaw will be braced, and usually the poll and neck will also be braced. A horse comes above the bit for many reasons - 99.9% of which are rider created and nothing to do with the horse 'being naughty'.
A horse being behind the bit is a huge pain in the backside, and very difficult to correct. Its head is behind the vertical and hyperflexed longitudinally over the neck. Often the horse will also be blocked in the base of the neck, and the hind legs won't be engaged. The reins will feel loose, and the rider will have no contact with the bit. The horse may open its mouth or refuse to take contact.
However, this should not be confused with riding a horse deep. An experienced rider can ask a horse to come a little deep in training, rather than being on or slightly in front of the vertical consistently. The horse must have a very good understanding of working through from the hind legs, and the hind legs must remain active while the horse is deep in front. This positioning will help to soften and lift the horse's back. It is good to ride a little deep, a little low, a little long, a little open, a little short etc. through your training sessions, rather than always in a competition frame. This creates a more adjustable, loose and elastic horse.
I hope this helps you!