I've always seen friends putting leftover, cooked food in the fridge with food wrap. I asked them why they are doing it and they don't even know why they are doing it. It is necessary to put just cooked food in the fridge with food wrap?
Wrapping food in plastic wrap before refrigerating has a few obvious benefits:
1) keeps the food from drying out in the fridge.
2) prevents odors (garlic, onions, fish, etc.) from transferring between the item in question and everything else in the fridge.
3) keeps crumbs, extraneous particles from falling into the food. If there were a lot of mold/microbe life already proliferating in the other refrigerated goodies, it might even serve to slow down slightly their penetration into your new leftover food on intra-fridge air currents (...ovbviously I'm reaching here)
But no, you don't have to use the plastic wrap; it's just a custom.