The anthropic principle is most generally a principle in a theory that takes into account an observer. Such as in quantum mechanics, where it must be asked whether or not the presence of an observer influences what is being observed. The anthropic principle is also a broad concept encompassing many dressings of the essential idea that the universe happens to be the way it is to allow for the emergence of intelligent life. Basically, to move into mixed-metaphor, there's a fallow energy that has been cultivated with physical laws that create enhanced circumstances, give advantage to, exclusive advantage to, make almost impossible the not-emergence-of, life, and intelligent, conscious life for that matter.
In other words again: The universal laws and characteristics of the universe are all the way they are to allow for the existence of intelligent life.
The foundation of this principle is based upon the observation that it has taken a remarkable set of coincidences to allow for the formation of carbon-based life in the universe. Even beyond our improbable local situation that finds Earth in the habitable zone, the right size, etc., that heavy elements have formed in the first place to allow for the formation of galaxies, planets, and eventually people.
It may also be worth mentioning that the anthropic principle and intelligent design are not necessarily synonymous. Intelligent design implies a god, the anthropic principle can simply take the "self-consciousness" of the universe into account, with observers providing the consciousness; and so we can wander into philosophy...and so it may be better to say that the anthropic principle takes the observer into account, as part of the system being studied.
There are two popular forms that the anthropic principle comes in: The Weak Anthropic Principle and the Strong Anthropic Principle. Each one revolves around the ideas mentioned above.