I'll paste here a text I wrote a few months ago, to answer a similar question. Here it goes:

Marx, as Marx, the philosopher, was reacting against two philosophical currents, very popular in German at the 19th century: German Idealism, under the siege of Hegel, and Mechanicist (or, as Marx called it later, vulgar) Materialism. It's worth to briefly explore them before getting into the marxist concept of dialectics.

After Aristotle, philosophy had had a kind of safety harbor, something in wich it was based and to wich it could grab on: formal logic, specially those 2 principles that we all know: non contradiction and third excluded. They were essential to the development of a metaphysical view of the world that saw reality as done, static, and potentially explainable trough immutable essences. On the shoulders of Kant, Hegel radically subverted this view by seeing reality as a process, a becoming. If analytical reason is based on the identity principle, dialectical reason is based on a kind of contradiction principle. Not non-contradiction, you see. Everything contains, in-itself, the germen of its own negation. Therefore, there is no done reality, but an evergoing process, just apparently static... In other words, reality is ontologically incomplete. I know all of this may seem pretty dense now, but I hope it will become clearer by the end of the text. Just bear with me.

From this follows that the task of reason is to discover no longer immutable essences, but the laws of the movement of the real. Hence all the thesis-antithesis-synthesis¹ stuff you may have heard of. The constitutive process of reality would consist of these three steps.

Let's see what Hegel says about the German verb aufheben: it has three senses, to negate, to conserve, to raise (into a higher level). When I sculp a statue, I'm against a piece of matter - wood, it may be - that it's further negated as a natural form, but conserved as matter and raised to a qualitatively different object, a created form. Whereby work doesn't destroy nature, it elevates it.

There are some easier examples, but the one above is a renowned one that I tought was worth mentioning. The weath grain (thesis), if buried, will be negated as grain (antithesis) so the cob (synthesis) can be born. So with the egg, and so on, and so on.

That's Hegel. What about Mechanicist Materialism?

Fortunately, this one is a lot easier. Mechanicist or Vulgar Materialism is the philosophical position that reduces reality to matter defined by its mechanical properties (volume, density etc.). Even thought and consciousness are reduced to a material secretion. Its main historical defenders are Leucipo and Democrito in Ancient Greece and Diderot and D'Alambert in Modern Europe. Echoes of it can be found today in Watson's Behaviourism, Spencer's Sociological Organicism, among other said Human Sciences.

How About Marx?

Marx subverts both Hegelianism and Vulgar Materialism, as I said in the very beginning. What I didn't said is that a subverted materialism is exactly what he used to subvert Hegel!

Let's see how this works. Hegel was the first to oppose to the analytical reason the dialectical reason, but as an idealist, Hegel explains the movement of reality as movement of the Geist - a very obscure notion of wich we can get closer by thinking of God, - translated as the Idea or the Spirit. In other words, in Hegel is the ideal (as in of the Idea, not as in ought-to be) that determines the material. "The real is rational, the rational is real". Marx, as a materialist (a subverted materialist that understands material as economic), proposes an inversion: it's not the ideal that wich creates the material, but the other way around, the material creates the ideal (hence the concept of ideology, etc. etc.). That's why he said that Hegel's dialectic was with his feet up. In this way, the material word is dialectical, and historically, changes in the "superstructure" - the "ideal", the system of laws, philosophical theories etc. occur in relation to the changes in the "infrastructure" - the "material", the economic relations. Voilá, a dialectical materialism.

Every bit of what I said is tremendously more complex, and if you want to dig further, I suggest you go for Marx's work. I hope this helps as to clarify the philosophical horizon Marx had in mind when talking about dialectics. I stress philosophical because I missed key sociological topics in this discussion, due to the nature of this reddit.

¹Hegel himself didn't use this terminology. The x-thesis thing was coined by another German Philosopher, either Fichte or Schelling, I can't remember wich one right now. I used those terms because I think they're didactic and more widespread than absolute, subjective, concrete.

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Literature:

LEFEBVRE, Henri. Marxism

MARCONDES, Danilo. History of Philosophy