Talking is what we do when we speak words out loud. Your teacher probably forbids talking when students are taking a test. Shh!
Are you having a discussion? Giving a lecture? Issuing commands to your dog? These are all examples of talking, using the power of speech to communicate. When you give someone a talking-to, you scold them, and if you start a sentence with talking of, what you mean is "continuing with the subject at hand, there's more I'd like to say," as in, "Talking of puppies, I was thinking we should get one!"