In English grammar a 'linking verb' is an intransitive verb that requires a 'subjective complement'. Such complements are either predicate nominatives or predicate adjectives.
Agamemnon is king. The verb 'is' links the subject to the predicate nominative 'king'.
Achilles seems unhappy. The verb 'seems' links the subject to the predicate adjective 'unhappy'.
In Greek, as in English, there are several verbs besides 'to be' that may function as 'linking verbs': become, seem, feel, look, appear, etc.
Greek grammars typically call such verbs 'copulatives'.