A linking verb is a verb which links or establishes a relationship between the subject and a term in the predicate which describes or renames the subject.
It does not show action, but, rather, it links.
The common linking verbs are be, appear, become, feel, seem, smell, taste, and sound.
Please note that be may also be an auxiliary verb. All the others except for seem can be transitive or intransitive action verbs.
One way of testing for a linking verb is to replace the verb with the appropriate form of seem. If the sentence is still saying pretty much the same thing, the verb is a linking verb.
Action Verb:He tasted the ice cream. (action)
Linking Verb: The ice cream tasted good.
(Tasted is used to help good describe the subject.)