"To be or not to be?" In his most famous line, Hamlet was using the infinitive form of the verb "be." The infinitive form of a verb is its most basic form, usually its "to" version.
The word infinitive comes from the Latin infinitus meaning "unbounded, unlimited." When a verb is in its infinite form, it's not limited or bound by its subject or tense. Contrast "to be" with "was" — was is tied to the past tense and a single person. Strip away the word to from "to be" and you have what's known as a bare infinitive. Keep the to there and you've got a full infinitive.