Putting it plainly, if you can train a body part the next day then you haven't trained it properly in the first place.

Following on from what Benni has already said the reason for not doing it day after day is because you need to recover. Of course you can lightly train muscles each day like a cyclist would ride a bike everyday but its a different sort of training. They are fatiqueing thier muscles and they grow a little for endurance, but not alot as the muscle is more efficent smaller as it uses less energy. If not a marathon runner would be a giant but a sprinter who only uses the muscles for 10 seconds would be a weakling. A bodybuilder is breaking the muscle fibres down so that they repair over the top of the broken fibres and therefore grow and repair stronger.

Yes you can lightly train or endurance train and see an improvement as the muscle is growing from doing nothing to now being a better engine. However this growth will be minimal and will not continue.