Flat roofing is roofing where the slope or pitch of the roof is barely noticeable. All roofs have a slope to them because that's what lets rain run off the roof instead of forming a puddle -- you just can't really see the slope on a flat roof. Flat roofs work well in some cases, but they aren't meant for all buildings.
Stuff On The Roof
Flat roofing works best for buildings that will have things on the roof. For example, a commercial building might have a huge air conditioning compressor on the roof because there's no room down at ground level for something of that size. Or, the building might have an observation deck or outdoor seating area for a restaurant that's in the building.
Homes and apartment buildings can have flat roofs, too, because these are often the easiest for maintenance workers to use. If you have a large apartment complex, you'll need that flat roof for compressors and work areas when fixing leaks.
Flat roofing is not appropriate for residential homes in areas where there is heavy snowfall. You will still see commercial buildings with flat roofing, but on buildings with smaller square footage, a peaked roof is more appropriate. Too much snow accumulation can weaken the building and increase the chances of a collapse, and a slope allows you to remove snow with a roof rake.
In sunny areas, a flat roof allows for larger overhangs. If you have a sloped roof and want to provide shade, those overhangs are going to look a bit strange. Either you'll have a sloped roof with a flat overhang, or a sloped overhang that creates crevices that are perfect for pests to hide in. Flat-roof overhangs, though, look a lot more open and are less visually jarring.