The water pressure inside plant cells is called turgor pressure, and it is maintained by osmosis.
Turgor pressure within cells is regulated by osmosis and causes the cell wall to expand during growth.
Along with size, the rigidity of the cell is also caused by turgor pressure; a lower pressure results in a wilted cell or plant structure (i.e. leaf, stalk).
One mechanism in plants that regulate turgor pressure is its semipermeable membrane, which only allows some solutes to travel in and out of the cell, which can also maintain a minimum amount of pressure.
Other mechanisms include transpiration, which results in water loss and decreases turgidity in cells.
Turgor pressure is typically said to be caused by the osmotic flow of water.