Damage to the kitchen ceiling would typically be repaired with drywall, not plywood. The bigger question is what caused the damage. Usually damage to the ceiling is caused by water. The only way to find out is to remove the plywood and look up into the ceiling space. If this is a 2-story property, I would look to see if there was a bathroom above the kitchen. There could be a leak in the supply and/or drain lines in the bathroom causing water to come through the ceiling below. It is also possible that the grout and/or caulking in the shower surround has failed and water is getting into the wall and traveling down to the kitchen. Maybe there is no problem with the plumbing or the grout but the tub or sink overflowed. If there is no bathroom above the kitchen, I would look in the attic to see if water is getting in from an old roof. You best bet is to hire a home inspector to get to the root of the problem. It could be minor or could be major. Repairing the ceiling properly wont cost much... but what are you going to do to keep it from happening again?