An air wave is simply the sound or acoustic wave created by the source, which by definition is what travels through the air rather than the ground. It is what you hear. In most cases, the seismic velocity of the near surface materials his higher than the velocity of sound in air. But in some cases the air wave is faster, and can arrive at the geophones before the seismic first break. This can make the first breaks difficult to pick.
An example of an air wave is shown below. The traveltime graph of an airwave is linear, and will be about 330m/s. It is generally lower in amplitude and higher in frequency than the first break, and can generally be dealt with in processing using a low-cut filter.