To "keep someone waiting" means to make them wait for a while. Use it like this:

They kept me waiting for over an hour. I was furious!

When you use "keep" in this way, it means to make something continue. So to "keep" a person waiting means that you've made them continue to wait. Another example is "keep (someone) guessing" which means that you do a lot of confusing things, so the person has to continue to guess what you're going to do next.