To make someone believe, or feel sure about something, especially by using logic, argument or evidence.
The overall goal of a persuasive speech is for the audience to accept your viewpoint as the speaker. However, this is not a nuanced enough definition to capture the actual goals of different persuasive speeches. Persuasive speeches can be designed to convince, actuate, and/or stimulate the audience.
A convincing speech is designed to cause the audience to internalize and believe a viewpoint that they did not previously hold. In a sense, a convincing argument changes the audience's mind. For example, suppose you are giving a persuasive speech claiming that Coke is better than Pepsi. Your goal is not just for the audience to hear that you enjoy Coke more, but for Pepsi lovers to change their minds.
An actuation speech has a slightly different goal. An actuation speech is designed to cause the audience to do something, to take some action. This type of speech is particularly useful if the audience already shares some or all of your view. For example, at the end of presidential campaigns, candidates begin to focus on convincing their supporters to actually vote. They are seeking to actuate the action of voting through their speeches .
Persuasive speeches can also be used to enhance how fervently the audience believes in an idea. In this instance, the speaker understands that the audience already believes in the viewpoint, but not to the degree that he or she would like. As a result, the speaker tries to stimulate the audience, making them more enthusiastic about the view. For example, religious services often utilize stimulation. They are not trying to convince those of another religion to switch religions necessarily; there is an understanding that the congregation already accepts part or all of the religion. Instead, they are trying to enhance the degree of belief.