What make electric charge to flow ?

Potential difference or difference of electric pressure makes the electric charge to flow.

Let we can make it clear ,charges do not  flow in a copper wire by themselves ,just as water in a perfectly horizontal tube does not flow .We know that if two vessels containing water to different levels are joined together the water flows from the vessels containing water a t a higher levels to the lower level. there is a pressure difference between the two ends. This flow of water continues, till both the vessels have water at the same level.Thus ,in flow of the water from one vessel to the other ,the direction of flow of water is determined by the level of water in the vessels. In a similar manner  if the two charged conductors are joined  by a metal wire ,the direction of flow of  electron is determined by a quantity called the potential of the conductor. The gravity has no role to play in the case of charge flow.The electrons moves only if there is potential difference.