A bubble in water is a pocket of gas surrounded by liquid water. The gas pressure pushes against the water nearly equally in all directions so bubbles are generally approximately spherical. Since the gas is less dense than the water, it rises to the top. When the bubble reaches the surface of the water, sometimes the surface tension keeps it trapped there.

There are many different reasons that bubbles form in water.
Carbonation - Carbonated water involves carbon dioxide dissolved in water at high pressures. When the pressure is released (e.g. a beverage container is opened), some of the dissolved carbon dioxide comes out of solution and nucleates bubbles.

Boiling - When water boils, it undergoes a phase change from a liquid to a gas. As the transition takes place, gaseous water molecules collect together (nucleate) within the liquid and form bubbles.

Chemical reaction - If an aqueous chemical reaction that produces a gas takes place, it will also create bubbles in water.

Soap - Soap itself does not create bubbles, but it acts as a surfactant in water, reducing the surface tension and allowing bubbles to form more easily and persist longer since they are more stable.