Interesting question. But first, let's make clear that in the process of boiling a kettle of water you will actually observe two types of bubbles. First, just as the water starts to get hot, a lot of bubbles will form down the walls of your water container. These bubbles are AIR. Normally water has a lot of air dissolved on it. This is what allows breathing to fishes and other aquatic beings. The solubility of gases decreases when the temperature is raised, and that is why the dissolved air bubbles go out from the water.

Then, as the boiling point of water is reached (100 degrees Celsius or 212 degrees Fahrenheit), water vapor starts to form inside the liquid in the form of bubbles. Remember that at boiling point water and its vapor are at equilibrium, that means that every molecule in the system has almost the same willingness to be in the vapor phase as in the liquid phase, so they very readily form bubbles inside the liquid.

The pressure due to the ocean of air we live under is about 1 bar or 100 KPascals (units denoting pressure). Liquid water undergoes a phase conversion (called boiling) at 373 K ( = 100 deg C) to steam ( water in the vapor, or gaseous state of matter); this is because the water pressure of the steam equals the pressure of the Earth's atmosphere (mainly containing Nitrogen and Oxygen gases) at 100 deg C. When this happens a tiny gas bubble "nucleases" spontaneously within the liquid water, and the bubble grows and rises in the liquid until it pops out at about 1 bar of water vapor pressure.

Anyway, that is what boiling is. What do you think ice is ??

When you have water (or any liquid) in a container there is a constant process of some of the liquid evaporating into vapor and some vapor condensing into liquid. In equilibrium, these two processes exactly cancel and you have liquid with some vapor over it. The equilibrium pressure of that vapor depends on temperature(as well as the particular liquid).

As you heat up the liquid, the vapor pressure rises. At 100 degrees Celsius (212 F) the vapor pressure of water is about equal to the atmospheric pressure at sea level. At that point, as water evaporates inside the container, the vapor pressure inside the bubbles is high enough to keep the bubbles from collapsing again from the pressure of the water around it. Then the bubbles rise (why?) and break the surface.

Hence boiling.

Some questions for you: Why does it take longer to cook (by boiling) food when in the mountains? Likewise, why might you use a pressure cooker?