An active verb is a verb whose subject does the action. In The dog chased the ball, chased is active because the dog performs it.
Compare the passive: The ball was chased by the dog. The subject, ball, receives the action instead of doing it.
Picture a news headline: The Huskies beat the Bears in the last game. The Huskies, the subject, do the beating. That makes beat an active verb.
Now flip it: The Bears were beaten by the Huskies. Here the Bears sit still and take the action, so were beaten is passive. Same event, different role for the subject.
People often mix up active verb with action verb. An action verb describes an activity, like run or lift. Active describes the verb's voice, meaning the subject does that action. Action verbs usually appear in active sentences, but the two labels answer different questions.
One boundary case: The soup smells good. Here smells does not report an action the soup performs; it links the soup to a description. Verbs like this are linking verbs, and they are neither active nor passive.
So if someone says a sentence has an active verb, check that the subject is doing something, not just being described. In She runs every morning, runs passes the test.