Linking verbs are verbs that do not express actions, but conditions or states, such as all forms of the verb "to be," and the verbs "to become" and "to seem." Their function is to connect the subject of a sentence to a word that identifies or describe the subject. Take a look at the following examples:
William is excited about his promotion.
The linking verb "is" connects the subject "William" to the word or adjective "excited" which describes the subject.
The winter scene was mysterious.
The verb to be "was" links the subject "the winter scene" to a word that describes it: "mysterious."
She seems sad
The verb "seems" links the subject "see" to the adjective "sad."