Oxidizing agents are substances that gain electrons in a chemical reaction. Because of this action, oxidizing agents are also known as electron acceptors.
Let's put this in more visual terms. We just learned that oxidizing agents accept electrons. Let's recall that electrons are particles that have a negative charge. When oxidizing agents gain a negative charge, it can be said that they are reduced, as shown in this diagram:
The reason why a substance is called an oxidizing agent is that it oxidizes another substance. This diagram shows that the oxidizing agent gains electrons from another substance, which is the reducing agent. When an oxidizing agent gains electrons, it gets reduced, and, as a result, oxidizes the reducing agent.
It gets a little confusing since similar words are being used throughout. Something that can help is this mnemonic device: