When boiling water, where does the air that fills up the never-ending bubbles come from?

Aha! How do you know it's air that fills these bubbles? Isn't there a cloud of steam coming from your boiling pot of water, with the bursting bubbles at the surface? Doesn't the water level go down in your pot if you leave it boiling for a long time? See where I am going?

The answer to the question is that it is not air that fills the water bubbles, but water! Water vapor to be exact. Water in the form of gas. Water turns to vapor when it is heated. The vapor is trapped in bubbles that form at the bottom of the pot. The bubbles filled with vapor rise to the surface of the pot, where they burst, releasing the water vapor into the air above the pot. There, the water vapor cools and turns into the steam you see coming off the pot.

The steam dissipates into your kitchen (sometimes ending up as water condensation on cold surfaces), and that much water is lost to the pot. Over time, the water level in the pot goes down.