the short answer
A synergist muscle is a muscle that assists the prime mover (the agonist) during a movement, either by adding force to the same action or by stabilizing a joint so the main muscle can do its job efficiently. On a biceps curl the biceps is the agonist, while the brachialis and brachioradialis act as synergists that help flex the elbow. Most compound lifts call on several synergists at once, which is why a single exercise trains far more than one muscle.
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.