Dialectics is a very old element of philosophy surrounding, at its simplest, the notion of two conflicting subjects resolving their contradictions into a higher, third subject. Thesis, antithesis, synthesis. Marxism uses Dialectics, specifically Materialist Dialectics, as the basic framework of analysis. Marx didn't invent dialectics, though, and neither did Hegel, the philosopher Marx built off of. Dialectics was common even in Plato's time, as much of philosophy was presented as a debate, a dialogue, a dialectic between two opposing points of view. Dialectics isn't exclusively western, either, though Marx was educated on Western dialectics and thus is most relevant in our case here.

The practical aspects come from insistence on the unity of opposites, such as bourgeois and proletarian, feudal lord and serf, but could just as easily be the seed negating itself into the tree, into the apple, into the seed of the next tree, not quite the same as the external conditions are never the same. It also analyzes subjects as they can only exist in the context of their surroundings, and as subjects come into being and un-being. Contradiction, in Dialectics, becomes the source of motion and change, and is inwardly driven.

There's also the concept of the negation of the negation. This process is a spiral, not a circle, each new concept further introduces and resolves with its own contradictions.

I wrote more about the subject here, though I really recommend Georges Politzer's Elementary Principles of Philosophy for a clear and straightforward introduction to Dialectical Materialism.