Interacting pedestrians in a crowd spontaneously adjust their footsteps and align their respective stepping phases. This self-organization phenomenon is known as synchronization. However, it is unclear why and how synchronization forms spontaneously under different density conditions, or what functional benefit synchronization offers for the collective motion of humans. Here, we conducted a single-file crowd motion experiment that directly tracked the alternating movement of both legs of interacting pedestrians. We show that synchronization is most likely to be triggered at the same density at which the flow rate of pedestrians reaches a maximum value. We demonstrate that synchronization is established in response to an insufficient safety distance between pedestrians, and that it enables pedestrians to realize efficient collective stepping motion without the occurrence of inter-person collisions. These findings provide insights into the collective motion behaviour of humans and may have implications for understanding pedestrian synchronization-induced wobbling, for example, of bridges.