Every verb has a base infinitive form. We think of the infinitive as the verb with the preposition to in front of it, as in to have, to hold, to love, to honor, to cherish. Infinitive phrases can act as (1) nouns, (2) adjectives, or (3) adverbs. The most prevalent use is probably the adverbial use. If the verb in the infinitive phrase is transitive, it can have a noun or pronoun attached to it as the verbal object. Also, within the infinitive phrase, you might find all sorts of modifiers. Adverbs can modify the infinitive itself; adjectives can modify any nouns present. Study these examples of each use:
He wanted to win the game. (infinitive phrase used as a noun, the object of the transitive verb want)
She's got a ticket to ride. (infinitive phrase used as an adjective modifying the noun ticket)
To win the tournament, Tiger Woods changed his swing. (infinitive phrase used as an adverb modifying the verb changed)
Controversy rages over whether you may split an infinitive by putting other words between the to and the infinitive verb. The short answer is yes. The so-called rule against split infinitives is simply not a rule. For a thorough discussion and a press release by the Oxford English Dictionary, study the section on Verbs in Parts of Speech on Grammar.com. Click here for the beginning of that discussion.
See present-participial phrase and past-participial phrase.