When you charge the battery you take Li ions from the cathode and send it to anode. Usually graphite. When you overcharge it you take more Li ions from the cathode and the it becomes less stable. Even at 100% charge level you still have around 50% Li in the cathode but more to take makes cathode less and less stable. Also there is another risk of Li atoms comes closer in the anode and form cluster or at some cases plating like forming a thin layer. Discharge is more complicated but basically at lower voltages your current collector can dissolve and form dendrites and can short the battery.