Think of your central nervous system (CNS) as a rechargeable battery. It has only a finite amount of charge to it. Every time you do a challenging workout, you are draining charge from your battery. If you overtax the battery, it won't provide the energy you need.
Aside from that, your muscles also experience a certain amount of damage when you train them with resistance. It is only microscopic damage to your muscle cells, but it takes time for that muscle to rebuild itself. If you never give yourself a chance to recover you will overtrain.
All that being said, if you carefully monitored your volume, you could technically train the same muscle every day. Olympic lifters certainly do, but it takes them years to build up to that volume. Don't base your workout on what some professional athlete does though. You have to pay close attention to your limitations and create a system that pushes your limits but allows you adequate time to recover.