In it's contemporary sense a cynic is a person who questions the motives of others. This would be an accurate description of me (sometimes, when I'm not being gullible - which happens more often than I'd like). Cynicism in this sense can actually be healthy but, when carried to extremes, can also be quite annoying.
It is usually not a good idea to be annoying.
In the classical sense, Cynicism refers to an ancient Greek philosophy. Its precise origins are somewhat foggy; also foggy is the derivation of the word cynic which has been associated with either or both cynosarges ("white dog," "quick dog" or "dog's meat"; the name Cynosarges refers to a temple/gymnasium intended for use by those who were not Athenian citizens - slaves, foreigners, and such) or kunikos ("dog" or "dog-like").
Whichever derivation one prefers, the association with dogs seems unavoidable. People of lower castes were likely thought of as being at the same level - figuratively - as dogs. Antisthenes (a non-Athenian) is considered by some to be the original cynic; he frequented Cynosarges and worshipped Hercules, who is believed to have been a central figure in Cynicism. Antisthenes was also known to be a rude and crude individual (dog-like?).
Antisthenes was followed by Diogenes of Sinope who fully embodied the label dog-like because he took rudeness and crudeness to greater levels than his predecessor: he believed in acting naturally, including performing various bodily functions in public. This would be before Port-a-Potties.
Ultimately, the cynic believed that the only thing important is to be virtuous, and the way to be virtuous was to act according to nature, where acting according to nature essentially became a matter of eschewing social conventions. Society and its accoutrements are burdens that prohibit one from acting freely and virtuously. Some have interpreted this as meaning self-control - a matter of discipline. However one wants to interpret Cynicism, I believe it boils down to a belief that one needs to be critical of the artifices forced upon one by society, focussing on acting as one ought to act.
But that is an entirely other matter.
(Thank you to the Internet Encyclopedia of Philosophy for the information on Cynics.)