I first encountered the 5 sets of 3, 2, 1 reps instruction here.
Some say those are movement timings for concentric contraction, pause and eccentric contraction. Somewhere else, there where theories about different combinations of sets and reps.
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It's an inverse pyramid strength-training workout. Although this seems to be fairly low reps, it's used to encourage muscles to build volume.
I wouldn't suggest hitting these kinds of reps though. Injuries are rampant when you load up on these weights.
A more appropriate strength and volume building routine would be 10-8-6 or even 8-6-4 reps, each with increasing weight.
After emailing bodybuilding.com, this was their answer:
When you are conducting 5 sets of 3,2,1 you will do a rep range of 3, add weigh do a rep range of 2, add weight and then do a rep range of 1. The low reps and high weight will help with muscle building. You should be very fatigued by the time you hit one rep.
None of these answers are correct when applied to the workout linked above.
The bodybuilding.com email response is also wrong when applied to this workout, I assume they have given a generic answer on what 5 x 3,2,1 means but it has nothing to do with the workout linked.
The workout calls for five sets of 3,2,1 reps in a rest-pause style of training.
This means you use a heavy weight that you could do for about 3-4 reps max, and crank out 3 difficult reps (you can just manage to do them). Then to get your breath back you rest for just a few seconds (10 seconds or so), then force 2 more reps. Then you rest a few more seconds, and do the final rep. It's a way of pushing you to do (3+2+1=6) reps with a weight that normally you can only do 3-4 reps with.
That is one set. You repeat this process 5 times to do 5 sets.
Note, this isn't the usual meaning of 5 sets of 3,2,1, but this is the meaning in this context and for this workout.