"To convince the audience" means to persuade or make the people who are listening or watching believe and agree with what you are saying or presenting. Full definition
Unfortunately, even their kind words couldn't convince audiences to tune in. (slashfilm.com)
Those who work in the arts must possess the ability to convey meaning and convince their audience what they are witnessing. (bbebooksthailand.com)
In it you must introduce your understanding of the topic, the reason you're doing the project, and must convince the audience of the necessity of the project. (writingaresearchproposal.com)