Dialectic is a conversational method of philosophical inquiry associated with Plato (and later philosophers).
The term is not clearly defined in the Platonic corpus, but generally refers to a discursive attempt to arrive at knowledge. Though it is often called the "Socratic Method," it should be distinguished from an elenchos which is the cross-examination method of inquiry primarily employed in the Socratic (or Early) dialogues. Unlike an elenchos, the dialectical method is designed to lead us out of ignorance to knowledge.
An excellent example of dialectic in Plato is found in the Meno (82bff) where Socrates asks a series of questions carefully designed to lead Meno's young slave to conceive the right answer to a geomentrical question.