Modal verbs provide additional meaning to the main verb of a sentence by expressing ideas like ability, permission, obligation, or possibility. There are several types of modal verbs including single concept modals like "can" and "may" which have one meaning, double concept modals like "may" and "must" which have two meanings depending on context, and modals used in the past like "could have" and "might have". Modal verbs are followed by an infinitive without "to" and do not conjugate or take auxiliary verbs. They are useful for expressing concepts like permission, obligation, advice, offers, and more in both present and past situations.