Gerunds are verb forms ending in "-ing" that can function as nouns, verbs, or adjectives. Infinitives are the base form of verbs preceded by "to". Gerunds are used after certain verbs and prepositions, while infinitives are used after other verbs to describe future events or purposes. Some verbs can take either a gerund or infinitive with no difference in meaning, while others have different meanings depending on which form is used.