Both the words “skeptical” and “cynical” refer to a doubtful mood, but what is the basic difference between them?
Skeptical means “having reservations”. Someone who is skeptical will not easily be convinced, will be hard to persuade.
The main meaning of cynical is “believing the worst of people”, or as NOAD says, “distrustful of human sincerity or integrity”. By extension, it has come to mean “doubting something will happen”, which can be somewhat close in meaning to skeptical in some cases, but not generally.
As an example, in the sentence “John is skeptical about the motorway extension”, you could replace skeptical with cynical without altering the meaning. In the sentence “John is skeptical about global warming”, you could not do this change. Likewise, in “John has a cynical attitude”, you could not use skeptical instead.