For a cyclist, the term "flat" might mean a smooth, level road to ride on, but more often than not if you hear that word while on a ride, it means somebody has a flat tire and the ride stops to complete the repair.
Ideally you would discover a flat tire while at home so you can repair it at your leisure. Usually it happens out on the road, maybe on the way to work, or as the sun is going down or as it begins to rain. You need to be prepared to do a flat tire repair in any situation.