This recrystallized ice forms only when the ice has been buried by 10s of meters. Glaciers are able to flow, though they are solid. This happens in two ways. Eventually, this ice starts flowing downslope due to gravity. It's just that the position of the toe is retreating, because ice is melting away faster than it is supplied from above.
Ice builds into a thick mound several hundred meters thick.
Then, because ice is a weak material, the weight of the ice itself causes the mound to spread laterally, forming a broad ice sheet, and the toe migrates to lower latitudes. The process is analogous to pancake syrup spreading over the surface of a pancake. Glacial Erosion - Ice itself is very soft, so it can't grind away rock. But as glaciers move, the ice plucks away rock and sediment from its substrate and this material becomes entrained in the base of the ice. Thus, the glacier becomes like sandpaper and grinds away at its substrate.