Whether you're repressing a feeling, an idea or even a revolution, you're almost always going to be taking advantage of the press in repress. To repress something is to "press it down" where it can't be seen, heard or even recognized.
Psychologists often try to help people recover memories that they've repressed so that they can feel free of them once and for all. What makes repress different from press is that repress is almost always used when you're talking about an idea, concept or something intangible. In other words, you repress, say, your emotions. You don't repress olives to get olive oil. However, you can repress someone or some group by intimidating them — like repressing the protesters by sending out cops on horseback.