Its because of a little something called refraction. This is when there is a change in direction of what we call a wave ( such as sonor waves or light) due to a change in its speed. Also, when one object has a different refractive index, meaning a different ``speed of light`` than another object it causes this refraction. So, since water has a different refreactive index then air, it changes the direction of the light basicaly ``bouncing`` of your face and onto the water which creates a reflection. You see the light waves which are changing direction creating an almost identical image to what is standing in from of it. All in all, water has a higher density then air so it causes the light to deviate. This deviation can also be proven when you put a spoon, for example, in a glass of water and the spoon seems detached or bent from the part thats in or out the water; it dosn`t look straight and the part under the water looks bigger and very weird. So voilà, the magic of physics and optics :P
The light waves reflect off of the surface of the water. Also, you can only see your reflection if what is underneath of the water is darker than you. An example, things reflect better off of water thats in a black cup, versus one in a lighter color.