The Synchronizer is a logic gate that functions as 2 RS Latches connected to an AND Gate. When its left or right sides are powered, the corresponding light will turn on and remain on even if the signal it received was a pulse. When both lights are on, it will briefly emit a redstone pulse, and then reset. It will also reset if its middle input is powered.
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A Synchronizer can be used similarly to an AND Gate, with one major difference. While an AND Gate requires multiple inputs being powered simultaneously to produce an output signal, a Synchronizer does not because it remembers the pulse it received before the second pulse.
If you try to use an AND Gate with two inputs that pulse instead of having a constant ON state, the inputs have to be sychronized for the AND Gate to emit an output signal. The Synchronizer allows a signal to pass even with inputs that are out of phase.
Two offset Timers give input signals to this Synchronizer. The left Timer has already sent a pulse which the Synchronizer remembers, as seen by the left red light. The right Timer is currently sending its pulse.
Having received both input signals, the Synchronizer sends an output signal to the lamp.