"Have to" is used to show obligation. "Must" has the same meaning but cannot always be replaced by "have to".
I have to wash the dishes because my girlfriend wants me to.
Infinitives are the "to" form of the verbs.
For example, the infinitive of the word "be" is "to be".
Infinitives are used as subjects, complements, or objects. Both Infinitives and Gerunds can be used as the object of the sentence, depending on the main verb.
For example, I want to go home, but Susan suggested going to the coffee shop.