Experiment to prove that water has air
There are two ways that I interpret the question you're asking, and I'll try to address each in turn.


If your teacher boiled a container of water and held a piece of glass above it to collect drops of liquid water, he or she may have been trying to show that water doesn't disappear when it boils, that instead it turns to a gas that can move through the air and can be condensed back into a liquid.  Essentially, $\ce{H2O}$ is $\ce{H2O}$, regardless of the state of matter it occupies.
If instead the teacher wanted you to observe the bubbles of gas forming in a container of hot or boiling liquid, he or she might have been on the right track, but either failed to convey the correct message to you or had the wrong idea in the first place.
If I take water from the tap and heat it strongly, bubbles will form on the inside of the vessel I'm heating it in prior to it boiling.  These are bubbles of gas that are no longer soluble because the temperature of the liquid is too high (and its pressure has decreased as compared to the tap.)  The gas is dissolved air (mostly carbon dioxide, I suspect) with a large portion of water vapor.  In any case, they are bubbles of gas that were dissolved but are no longer.  You can see this happen any time you boil a pot of water on the stove.  
Once the pot reaches boiling, any bubbles are almost exclusively gaseous water formed via vaporization.
An easier, if slower, way to see this is to run a cold tap until the water is as cold as it will get, then pour a glass.  As it sits (perhaps for an hour or two), bubbles will eventually form on the walls of the glass.  These eventually will dissolve again and the gas will escape through the top of the glass, so it's not something you can set up at night and come back to the next morning.  The bubbles are air that was able to dissolve in the high pressure/low temperature water in the pipes but not in the low pressure/high temperature water in the glass.