A category will have several judge pairs in a big competition. The Judge pair goes through the beers, and if they think there are some worthy of going to the second round they push those to mini-BoS. The beers selected go against the beers the other judge pairs selected. This puts the selected beers in a head to head tasting, which can equalize judge pairs that were strict or lenient in the scores. The beers have been judged, so no scores assigned, any defects picked up result in the beers being kicked out of the running (this is where the second bottle is used, and sometimes it has a problem). Style accuracy is a big factor. Eventually the final 3 are up for 1,2,3, and those are discussed and they are assigned places based on the judges impressions.
The judges that are in the mini-BoS are usually the ranking judges for the category that session. At the NHC you get GM, Master, National, sometimes Certified doing the mini-BoS.