To simplify something is to make it less complex and easier to understand. When you simplify, you make things clearer.
Since simple things have less parts or complexity, when you simplify, you're eliminating the clutter and reducing something to its essence. For example, if a speech is long and confusing, the person giving it might need to simplify their ideas: make them clearer. Teachers are good at simplifying; they take complex ideas and make them easier for students to understand. If you don't understand what someone is telling you, ask them to simplify it.