Named after David Premack. I have yet to find a perfectly clear definition of this idea. One of the most commonly given forms of this principle is "a more probable activity can be used to reinforce a less probable activity".
It seems that 'probable' is being used in a special sense here. The simple everyday way of putting it would seem to be "a more preferable activity can be used to reinforce a less preferable activity". I have never seen it stated this way, but this does seem to be what Premack meant.
An oft given example of this is that of two rats, one who is given all the water he can drink, but limited space to run around in, and one who can run around all he wants, but has limited water. The first rat will drink even more if he discovers that drinking the water will give him the opportunity to run, and the second rat will run even more if he is given water after running.
Doesn't look like much does it? But in psychology you have to name all the little pieces, no matter how obvious they seem. Also, the Premack principle shows reinforcement to be relative, not absolute. All that is needed is for the reinforcer to be desired.
The Premack principle is used in everyday life, especially with children (You may have some dessert after you finish your dinner). It's also often suggested as a method of improving your own behavior.
It will work best if the subject is given a choice as to what the reinforcer will be (The subject being the best expert on he desires). It is also a good idea to match the strength of the reinforcer (positive) to the strength of the activity you want to encourage (negative).
When applied to humans it is usually assumed that the reinforced behavior is intended to eventually stand on it's own, without the continued reinforcements.