Diagram: Firing a Heavy Weapon — if the firer remains stationary it can shoot up to the weapon's maximum range, firing the number of times indicated. If the firer moved that turn, it may not shoot at all.
Heavy weapons are heavy man-portable weapons such as heavy boilers or lighter weapons which need to be recharged between each shot, carefully set up or whatever. If a unit moves then it cannot shoot heavy weapons, they either move or shoot, but not both (remember that even if the model armed with the heavy weapon doesn't move it still can't fire if other members of its unit move). When shooting heavy weapons always fire the number of times indicated regardless of range in the same way as assault weapons. They are very good for laying down long-range supporting fire or knocking out tanks, strongpoints, etc.