The 555 works by allowing the capacitor to charge until the voltage reaches a certain threshold voltage that triggers the 555 to quickly discharge the capacitor then the process starts again with the capacitor charging up again. The frequency is determined by the rate of the charge and is synchronized like a phase-locked loop. Synchronization is achieved simply by feeding the sync signal into the trigger input via a capacitor to create a crude AND gate that forces the 555 to reset whenever there is a voltage change in the sync signal. When the sync signal is absent, the 555 continues to free run although at a different frequency due to impedance changes on the trigger input with an absent sync signal.