What does it mean?

Action verbs (also called dynamic verbs) refer to an action, see A, and state verbs express states or conditions which are relatively static, see B.

Action verbs can have both simple and continuous forms. State verbs are usually in the simple form. However, some state verbs can be used in both  continuous and simple forms, see C, if they:

→ refer to a temporary action (She is being immature.)
→ or an action in progress at a certain moment (She has been feeling exhausted lately.)
→ or when they have an active meaning. (The greengrocer is weighing the grapes on the scales.)