The popular view is that it's the quest to build an intelligent machine. This raises a number of questions.
These shade into questions about the nature of intelligence in general. Are there some characteristics that any intelligence, whether man, machine, or Martian, must have? In an essay on communication with extraterrestrial intelligence, Marvin Minsky in Why intelligent aliens will be intelligible (photocopy M131 in the library), has argued that there are - that any intelligence will divide the world into things versus actions and events, will have a notion of plan and goal, and will even have some idea of economics! Minsky believes the latter to be necessary whenever there is a limit on one's resources, which is always.
So which properties of our minds are universal? Surprisingly to those who see computers as coldly logical machines, the fact that we make mistakes, including mistakes in perceptual interpretation, is almost certainly one; and any intelligent machine will also do so. In the early days of computing, it seemed that one might be able to solve many problems just by blind search, trying out all possible solutions. In fact, the time taken to solve almost any interesting problem by this method grows exponentially with the size of the problem - the so-called combinatorial explosion, which I refer to when discussing chess. Work in game-playing, translation, and planning, amongst other fields, soon demonstrated that blind search isn't feasible except for very tiny problems. Instead, computer programs, like us, need to rely on cleverly coded real-world knowledge, on special tricks, on heuristics or rules of thumb that work most of the time but not always. In perceptual interpretation, it's often necessary to hypothesise on the basis of incomplete data.