A recovery run is a run that simply allows waste products from previous sessions to be flushed out of an athlete's system.
This isn’t very scientific, but basically when you hear someone refer to a recovery run it just means a short slow run to get rid of some of the stiffness that may have accumulated in your muscles.
This is a device most commonly used by distance runners, particularly those who are in a period of hard training (recovery runs may be done the morning after tough sessions).
It is important that this doesn't turn into "junk miles". The aim is not to work hard, nor to put mileage in the "bank", but to clear out waste products. Even for very long distance runners we'd suggest no more than 2-3 miles for a recovery run. Long distance runners can get into the mentality of thinking more miles is always better training - and use "recovery" runs to achieve this. This is not a good idea and will not result in improved performance.
Sometimes long distance runners, in particular, find it useful to jog in between hard runs in an interval session in order to keep moving, and so avoid having muscles stiffen up. This kind of running is very slow and can even be done on the spot.
You should not confuse this with Fartlek Training where the slower paced running is part of the session to work the lactate shuttle system.