Strictly, the study of duty, but in practice a particular view that duty is the primary moral notion, and that at least some of our duties (for example, keeping promises) do not depend on any value that may result from fulfilling them.
Immanuel Kant (1724-1804) is probably the most famous deontologist. Also see: categorical imperative.
Consequentialists (or other teleologists), by contrast, base all duties on the production of value; they treat all duties as ‘forward-looking’.
Deontologists normally treat at least some duties as ‘backward-looking’, in that their justification depends on a past event or situation, and some as neither ‘forward’ nor ‘backward-looking’, in that their justification appeals to some absolute rule (for example against taking life).