Now flash sync usually refers to when you flash fires in relation to your exposure. This is best demonstrated by imagining a long exposure, like 6 seconds. The flash can fire right after the first curtain of your shutter is completely open, or it can fire right before the second curtain of your shutter begins to close. For first curtain flash sync, your shutter will open and the flash will fire. For second curtain flash sync you shutter will open and the flash will wait until just before that six second mark to fire.
Both ways serve a specific purpose and creates a certain effect in the final image.
If your subject and your camera are not moving, then it won’t matter whether your flash fires in first curtain sync mode or second curtain sync mode. If there is motion, then having the flash fire in first curtain sync mode would illuminate the subject and freeze it at the point once the first curtain is completely open, and then ambient light will illuminate any motion occurring during the rest of the exposure.
Having the flash fire in second curtain sync mode would allow you to record motion until right before that second curtain closes when a burst of flash light illuminates the subject freezing them. You image could have all tell-tale trails behind the the subject in the final image.