Take a look at the entry on Wikipedia and the quasar's location in the sky:
https://en.wikipedia.org/wiki/APM_08279%2B5255

APM 08279+5255
Right ascension 08h 31m 41.70s
Declination 52° 45′ 16.8″

So you can see that the numbers basically tell you the position in the sky, more about that in a second.

First, APM means the source for this particular object is the Automatic Plate Measurement catalog system. It scanned plates from telescope observations, and found this particular object, which is referred to later in important papers about this object.

The remainder of the numbers are the "longitude" or Right Ascension in hours, minutes, and fraction of seconds (08h 27.9') and the "latitude" or Declination in degrees and minutes (52° 55'). This is referenced to the B1950.0 epoch which is a snapshot moment in time that everything can be referenced to, since stars, galaxies, etc are moving relative to one another (Big Bang expansion, galactic rotation, etc, etc) and this results in changes in sky position over time.