If you overfill your engines oil pan with too much oil then you could potentially blow out oil seals or damage your engines oil pump.
If you happen to add just a 1/2 quart of oil over the fill mark then usually nothing bad will happen and if your car uses oil then the oil would burn out of the engine after some driving so I wouldn't worry about it.
However if you added a quart too much of oil then you should drain the excess oil out of the engine to prevent damage to the engine.
The engine needs just the proper amount of engine oil to circulate through the engine and when there's too much oil in the engine oil pan then the engine cannot circulate the oil properly.
When you overfill the engine with too much oil the engine can suffer severe damage and your engine can eventually lock up as a result.
If you overfill the engine oil more than a quart then you need to drain the extra oil out to prevent damage to the engine.