Dialectics is, in marxism, the movement of material things and ideas through internal contradictions.
The word "dialectics" initially meant, primarily, the art or the science of argumentative discussion.
To Hegel, dialectics is the movement of the idea, going through sucessive steps: thesis, antithesis, synthesis, until the absolute idea. To Marx and to marxists, however, it's not the movement of ideas, it's the movement of things themselves through contradictions, and that the movement of ideas is just the conscious expression of matter itself.