Here is a quick piece of training terminology you might here thrown around at the gym.
Back-off Sets - Sets done for less weight and/or less reps after a lower-rep set of the same exercise, often with higher reps.
1 set of 5 @ 70% of your training max (work set #1)
1 set of 5 @ 80% of your training max (work set #2)
1 set of 5 @ 90% of your training max (work set #3)
1 set of 15-20 reps @ 60% of your training max (back off set)
Or the same as above, but after work set #3 you might repeat work set #1 twice - they would also be back-off sets.
Work up to a heavy single.
One set to technical failure of 50% of your single.
What is the difference between back-off sets and accessory work?
It's a fuzzy line. If it's the same exercise, I consider it a back-off set. If you switch to a new lift, or a new grip, or take a break and then do a totally different sets/reps/rest scheme, it's more like accessory work.
So if you do three sets of weighted chin-ups and then a set of unweighted chinups, I'd call it a back-off set. If you do those three sets and then do pulldowns or rows for higher reps and a lighter resistance, I wouldn't refer to it as a back-off set.
Hopefully this keeps you talking the same language as the other folks at the gym.