How Hegel's Dialectic Works

Imagine that there was a baby who was born without an arm. In this story, medical science has perfected the growth of limbs, and so creates an artificial arm, mechanical on the inside, but upon which her own flesh takes hold and grows.

At first, the child grows up thinking that the arm is nothing but a part of her. She and her arm are of the same person; there's no distinction between them, and no reason to suspect anything. This thinking is true on her part, but not understood, because she only thinks that her arm is such immediately, that is, nonreflectively; she hasn't reasoned out the reason why the arm is hers. This is the Hegelian thesis.

Then, one day, the child, now an adolescent stumbles upon the medical records of the procedure that gave her her arm. She finds out that this arm is actually a special thing, something that is separate from her. She repels from it, calls it "the robot arm," and no longer considers it a part of her. This is the rejection and distinction of the Other as Other, the antithesis.

Eventually, the child, who is now a young adult, realizes that, whatever may be the case about the machinery in her arm, it's still her arm; it's the arm that moves when she wants it to, can move on mere intention without command, and which her own flesh has grown onto. While the arm still has its particularity, its Otherness, it is also reconciled back to the person; the arm is a part of the one again. This is the synthesis.

If you're Hegel, life, the universe, and everything works the same way.