the short answer
The agonist is the prime mover, the muscle producing the force that drives a movement, and the antagonist is the opposing muscle that lengthens under control as the agonist shortens. On a biceps curl the biceps is the agonist and the triceps is the antagonist. Reverse the movement on a triceps pushdown and the roles flip, because the labels describe what a muscle is doing right now, not a permanent job.
This article is general training education, not medical advice. Anatomy varies from person to person, so treat the examples below as the common pattern rather than a fixed rule.