The correct answer is - infiltration.
When the water from a rainstorm seeps into the ground, that process is called infiltration. The term infiltration is set because the water is literary filtrated through the ground as it moves through it, until it reaches its final destination.
This process is part of the water cycle, at least most of the time. Even though most of the water from the process of infiltration ends up as a spring, or enters some body of water, smaller part of it remains underground, as groundwater. The only way that the trapped groundwater would have been able to return on the surface and be part of the water cycle again would be if some geologic activity exposes it. Nowadays though, that role is the hands of the humans, as most of this water is used and pumped out for the usage of the human populations.
