There are several different ways that the body can deal with water intake.
The kidneys filter it out by pushing it through ureters to the bladder, to be excreted as urine.
The intestines absorb some of the water into blood vessels called lacteals or lymphatics, which return it to circulation to be used by other parts of your body.
Some still reach cells through osmosis. Your cells “inhale” fluid from both their external environment and also intracellularly stored supplies, in order to maintain osmotic balance and respiration (to make sure you can breathe).