Water stays on this planet due to gravity.
For any two objects or particles having non-zero mass, the force of gravity tends to attract them toward each other. In addition, the greater the mass, the greater is its gravitational pull. The gravity of the Earth pulls objects to its centre.
The Earth and water particles both have mass. Water, having a significant lesser mass, gets pulled towards the centre of Earth.
If gravity is a force that pulls everything towards the centre of the earth, you might wonder why don't kites get pulled down to earth?
The force that stops a kite from falling down is called lift - the force pushing the kite away from the surface of the earth. It is produced by air moving over the top of the kite at a faster speed than the air that is moving over the bottom of the kite.
Bernoulli's Principle (named after Daniel Bernoulli), states that the higher the velocity of a liquid, the lower the pressure it exerts. This also applies to air and is what allows kites, airplanes, space shuttles, and even plastic discs to fly.
There are many possible kite shapes but are generally designed so that air will be slowed down if it is travelling under the lower surface of a kite and will speed up if it is travelling over the upper surface of the kite.