The shutter in most SLRs (and mirrorless cameras) is a focal plane shutter. One "curtain" opens, then a 2nd "curtain" closes behind it. For most photography it doesn't have much of an effect.

For flash photography it can have some interested implications.

First at faster shutter speeds the 2nd curtain will start closing before the 1st curtain has opened all the way. So the exposure happens as a slit between the two curtains passing across the sensor/film. If you were to fire a basic/crude flash during this, you'd see shadows on the picture where the flash exposure was hidden by the shutter curtains. The fastest shutter speed where the 2nd curtain closes after the 1st is completely open is called "X-Sync" speed, this is the fastest shutter speed you can use with a basic flash exposure. Any faster and you'll either get shadowing or you'll have to use a flash capable of "High Speed Sync."

2nd is if you're doing longer exposures, the question is when do you want the flash to fire, at the begining of the photo or the end. In most applications, you probably want it to fire as soon as possible after you press the shutter (first curtain) but for very long exposures the opposite may be true in some situations. If the subject is moving in a predictable fashion (like a car moving in a straight line) if you took a longer exposure with th flash firing on the 1st curtain opening, it would "freeze" the car and then the car would continue to move and it's headlights/taillights would create a trail moving in front of where you froze the car (looks weird). In this case you'd want 2nd curtain flash that fires and freezes the car at the very end of the exposure.

Conversely if you're at a party/club and photographing people but using a longer exposure to get some of the lights in the background. those lights are not moving in a consistent pattern. Here using 2nd curtain doesn't give you an advantage and it might actually cause problems because you'll be freezing the people a bit after you press the shutter, they might even hear the shutter open or see the flash do a metering pre-flash and think the picture has been taken and then move, then the flash fires and freezes them breaking pose.