What do you call the process of water seeping into the ground?

Process of seeping (flow or leak slowly through a porous material or small holes) of water into the ground is called infiltration. Infiltration is the process by which water on the ground surface enters the soil.

Water not used by plants moves deeper into the ground. The top of the water in the soil, sand, or rocks is called the water table and the water that fills the empty spaces and cracks is called groundwater. Water seeping down from the land surface adds to the groundwater and is called recharge water.

Hence The process of water seepage into the ground is called Infiltration.