For DB curls for example say u can curl the 40's for 8 reps to failure. u would put them back on the rack and then grab the 35's and pump out as many reps as possible. put them down and grab the 30's..........all the way until you run out of db's. Hence the name run the rack.
there are many variations of this. some skip by increments of 10lbs, some stop after only 4 times, etc.