Air Guitar is a performance art, arguably for the musically ungifted. The performer holds an invisible 'axe' and proceeds to play it along with a piece of music - normally heavy rock.
The resemblance between the actual playing and air playing need only be tiny - the more important aspects being the facial expression, dance moves and often the complexity of solos. Of course, the more perfectionist air guitarist may attempt perfect air-fretting and strumming.
Air Guitar is also a competetive sport. The World Air Guitar Championships are held each year as part of the Oulu Music Video Festival, in Oulu, Finland.
If you're looking for a source of music to play air guitar to, then you could do worse than The Best Air Guitar Album in the World...Ever.
Update: Oh dear... it has been pointed out to me that air guitar players may be interested in a Jaminator - the device which allows you to actually play splendid riffs while completely lacking any talent.