| Confusingly enough, deontology has nothing to do with ontology. It is that branch of ethics, or ethical philosophy, which regards morality as arising wholly from duty or obligation. Deontological ethics, or deontics, stands in contrast to consequentialism, which holds that moral right and wrong arise from the beneficial or harmful consequences of possible actions. Utilitarianism is the best-known (though by no means the only) form of consequentialism.
Deontology finds its foremost exemplar in Immanuel Kant, formulator of the categorical imperative. Kant held that no action can be considered morally worthy unless it is done out of a "good will", and out of a feeling of duty. Actions performed for pleasure, personal preference, or other motives may have good result, but Kant believed they cannot be considered morally praiseworthy.
In a fully deontic system of ethics, such as Kant's, the actual consequences of actions are irrelevant in evaluating those actions' moral worth. Because we cannot control the future, the will or intention with which we perform an action must outweigh the result. While we can hope and aim for good results, we can't be held responsible for unintended ones. Moreover, the ends do not justify the means -- or the intentions -- in the slightest.
So where does this duty come from? Kant believes that moral duty cannot arise from a "hypothetical imperative" -- a conditional, consequential statement in if-then form. ("If you do thus-and-so, then happiness will increase," as utilitarianism might hold.) Morality requires categorical truth, an imperative which can hold for all people, in all situations. Kant finds this imperative in the command to "act only according to that maxim by which you can at the same time will that it should become a universal law."
A chief trouble of deontology is that it provides no solution to the moral dilemma that can arise from a conflict of duties. If we have a duty to follow maxim x and a duty to follow maxim y, and the two rules require contrary actions, then we are stuck. Another trouble is that Kant's ethics in particular rule against some actions which most find morally acceptable in everyday life -- such as the telling of "white lies".
Sources:
http://truth.wofford.edu/~kaycd/ethics/deon.htm
http://www.utm.edu/research/iep/k/kantmeta.htm
Discussing Kant with my GF, who's a grad student in philosophy | 
