As their name not-so-subtly hints, intensive pronouns are pronouns meant to intensify or emphasize the subject. Thus they are also sometimes called emphatic pronouns. Intensive pronouns function as appositives in that they rename, or rather repeat, the subject. The intensive pronouns are myself, yourself, ourselves, himself, herself, itself, and themselves.

The principal himself gave me permission to leave.
I myself will get the job done.
The students themselves are responsible for their homework.

Intensive Pronouns vs Reflexive Pronouns

You may have noticed that intensive pronouns are the same as reflexive pronouns and the two only differ in grammatical function. Intensive pronouns only serve to emphasize the subject, while reflexive pronouns serve as objects when the subject is doing an action to or for itself. An easy way to tell if a pronoun is intensive or reflexive is to simply remove it from the sentence and see if any necessary information or sense is lost. Appositives only rename or repeat, so intensive pronouns can be removed without ruining the grammatical structure of the sentence.

The CEO himself will inspect your work next week. (intensive pronoun)
The CEO hurt himself on the stairs. (reflexive pronoun as a direct object)

In the first sentence, the CEO is not inspecting himself, so himself is not a necessary object. Himself only serves to emphasize that the CEO is the one doing the action. We could remove himself entirely from the sentence, and everything still makes perfect sense:

The CEO will inspect your work next week.

In the second sentence, himself serves as a direct object. Who or what did the CEO hurt? He hurt himself. If we remove himself from this sentence, it no longer makes sense, because the pronoun is a necessary object.

The CEO hurt on the stairs.

Let’s consider a couple more sentences:

Mother herself couldn't have made a better dinner. (intensive pronoun)
Mother bought herself some chocolate yesterday. (reflexive pronoun as a direct object)

As you can see, the test we did before isn’t quite as foolproof when it comes to indirect objects. We could remove herself from either of these sentences, and everything would still make sense. However, if we remove herself from the second sentence, some information is lost, and the grammatical structure is changed. When we just say, “Mother bought some chocolate yesterday,” we lose the information telling us who she bought it for because we no longer have an indirect object.

If significant information is lost, or a sentence becomes nonsensical by the removal of the pronoun in question, it is a reflexive pronoun. If removing the pronoun makes no important difference other than losing some emphasis, the pronoun is intensive.