For the ancients, dialectic was largely a matter of philosophical method.
As embodying a theory about reality the term belongs primarily to Hegel, who thought that both reality itself and our thought about it (which were ultimately the same thing) developed by certain processes occurring (the thesis) which contained within themselves the seeds of their own frustration and destruction (the antithesis).
This antithesis, however, contained its own antithesis (the negation of the negation) which emerged in the form of a synthesis of the original thesis and antithesis. This synthesis then formed the thesis for the next stage in the overall process.
Marx took over the general ideas but replaced Hegel's idealist equation of thought and reality by his own dialectical materialism, applying the above process to the material world. This becomes historical materialism when applied to the development of societies and to human motivation, both of these resting ultimately on economic considerations.
Within psychology, dialectic may be described as any complex process of conceptual conflict or dialogue in which the generation, interpretation and clash of oppositions leads to a fuller mode of thought. It is not a prominent theory within the discipline, except in developmental psychology of the lifespan.
M P Honzik, 'Life-span Development', Annual Review of Psychology, vol. xxxv (1984), 309-31