As native English speakers we hardly ever think about parts of speech, but verbs are an extremely important element of our language. We need to describe our actions and the actions of others around us. Verbs allow us to do that. However, they don't always function as a mere action appellative.

Function

A copula verb, also known as a copular or, more commonly, as a linking verb, is a special verb in the English language that connects the subject of a sentence to its modifier--the predicate. Copula verbs do not describe actions, and they are not followed by adverbs. Let's take a look at the most common copula verb in the English language, the verb "to be," and use it to examine its function in a sentence. The car is green. In this sentence, green is not an adverb, that is, it doesn't modify the verb is, but rather, it modifies the noun the car (the subject of the sentence)--the car here is not just any car but a green car. This same concept carries over to larger sentences with more complex modifiers. For example: The green car is the same one my brother had when he was young. The predicate "the same one my brother had when he was young" is a phrase that modifies "the car." It is long and cannot be used as an adjective like "green" in the previous example, but its basic function is the same--to modify the subject.

Exclusively Copula

The verb "to be" functions solely as a copula verb, as do the verbs "to become" and "to seem." For example: The man becomes frustrated. The frustrated man became more and more morose as the day went on. It seems impossible. The impossible feat seemed to take forever to complete. The phrase "to take forever" colloquially means interminable, or lasting a very long while, and in this case modifies "the impossible feat," making it interminable.
These are verbs that will always be used to modify a noun.

An Exception

The one exception where the verb "to be" is not a copula verb is when it can be replaced by the verb "to exist" (i.e.: I think, therefore I am).

To Copula or Not to Copula

Some verbs function both as copula and action verbs. They are: "to appear," "to feel," "to grow," "to look," "to prove," "to remain," "to smell," "to sound," "to taste" and "to turn." A good trick for knowing when these verbs link subjects and their predicates and when they express an action is to replace them with the verb "to be" and see if the sentence still makes sense. It does not necessarily have to have the same meaning, but it has to be readable. For example: Sandra feels sad on Sundays. vs. Sandra feels that her opinion is better than yours. Replacing "feels" with "is" would give you: "Sandra is sad on Sundays." Yes, that makes sense. Meanwhile, the second sentence would give you "Sandra is that her opinion... ." Obviously, nonsense.

Expert Insight

If you ever get confused as to whether something functions as an action or as a link between a subject and a predicate, be mindful of what follows it. For example: This topic appears difficult. Here, the verb "appears" connects the subject "this topic" to what kind of topic it is, easy, green, airy... difficult. This difficult topic suddenly and clearly appeared to me. Here appeared is describing the action of "the topic." Yes, it appeared to me specifically, so you may think that that modifies the topic, but if you remove "to me," you'd see that it doesn't affect "the topic" at all. (This difficult topic suddenly and clearly appeared.) Therefore, in this case, appeared does not link the subject to any modifiers but describes its action.