Artificial Intelligence can be defined as
A computer doing something that we humans are capable of, without knowing how.
Limited to mental activity, that is. It's tempting to limit it further, to cognitive activity, if it weren't for the fact that
nobody really knows what cognition is.
This incorporates the popular use of the word (used to describe the actions of computer players in games, for instance) where the ignorance is on the part of the human player, but does not extend to the game programmer; and the 'scientific' use of the word, where the goal is often to create a program that outsmarts its creator.