A heyday is a peak of popularity or success. If you hear someone say "Hey! Back in the day, I was the best boxer in the city! No one could beat me!" he might be remembering his heyday as a fighter.
If you remember a time in the past when you were doing something really well or getting a lot of attention or fame, you might be reminiscing about your heyday. A person or an organization — and even a thing — can have a heyday, or a peak time when everything goes well. The good news is that a heyday can come again and again, so while your heyday as student president might be just a memory, there might be a heyday as governor of your state years later.