The majority of an audience refers to the largest portion or segment of people who are watching, listening, or otherwise engaging with a particular form of media. This could be in reference to a specific group, event, or presentation where the speaker is trying to convey their message to others. The phrase "majority of one's audience" means that the speaker has successfully captured and maintained the attention of most of those who are present for their presentation. It suggests that the content being presented is relevant, engaging, and appealing to a large portion of the intended audience.