Infinitives and gerunds are verbs that are changed into nouns. An infinitive is a verb with "to" in front of it, like "to study", and is used for actions that have not happened yet. A gerund is a verb ending in "-ing" that acts as a noun, like "studying", and refers to actions that are already happening or have happened. It is important to use infinitives and gerunds correctly and not mix them, as infinitives refer to future actions while gerunds refer to ongoing or past actions. The document provides examples to illustrate the differences between infinitives and gerunds.