"Suppressing" an accent means hiding your natural way of speaking. It may help to learn that the word "suppress" means to stop something or hold it back. It's used in these phrases:
suppress a cough
suppress a smile
suppress your appetite
suppress an urge (to do something)
You usually can't suppress a foreign accent. For example, if you're from France and learning English, you have a French accent. You might be able to improve or correct your accent, but you can't suppress it. But some people can suppress their regional accent, like a Southern accent.