If you stay close to a glacier, you most likely wouldn't know its moving. Glaciers move but their movement is slow. It is believed that gravity is the cause of glacier motion. The glaciers flow in response to gravity. Glaciers also slide on their beds which make them move faster. Glacier motion can be fast (up to 30 meters per day) or slow (0.5 meters per day) but on the average, glaciers move around 1 meter a day.
The middle of a glacier moves much more faster than the edges this is because that the edges are held back by the friction between the edges and the surrounding land.
It is also believed that glaciers move because of the pressure from weight of the overlying ice causing it to deform and flow.