It's not something you specifically find a particular use for, you just use it when it makes a job easier for you.
Example, today I had some cap head screws that were jam-packed full of metal swarf (Pretty much the exact same situation that TFrench mentioned above) that would be difficult and time-consuming to remove with a pick or anything else like that. Put hand over the cap head screw, point air gun into the head of the screw, pull the trigger, blasts out swarf so you can properly get an Allen key into the screw head.
Another example, sanding down primed joinery. The amount of dust created doing this is quite something and you can't really pick it up effectively with any other means (In a reasonable time-frame), you could use a tak rag but it would clog up very quickly with the amount of dust. Just take the object outside or near an exit, blow it down, most of the dust is removed in no time at all.
I do blow down machines with it occasionally to help keep the 'heavy' dust and shavings off, only when the HSE isn't knocking at the door however 8-[