Snowshoes allow a person to walk around on snow covered ground without sinking down into the snow. While not all snowshoes will work for every person, any snowshoe that a person straps on should still provide some form of aide in traveling over snow cover.
They work through some basic physics. When a persons foot presses down on a pile of snow, it exerts pressure on it. If the pressure is too high, the surface of the snow will crumble, and the person's foot will sink down toward solid ground. That pressure is found by dividing the force applied by the person's foot by the area over which that pressure is applied. The force can be thought of as the person's body weight, that area can be thought of as the sole of the person's shoe.
With a normal shoe, or boot, that area would be rather small. Holding the person's body weight constant, the only way to decrease the pressure applied to the surface of the snow is to increase that area. Snowshoe's do just that, and in doing so, allow those wearing them to travel through the snow at a brisk pace.