What 'the pump' actually does for you
'The pump' is a temporary increase in muscle size during a workout from blood flowing into the working fibers. High-rep sets with short rest between them restrict blood leaving the muscle faster than blood coming in, so it literally pools inside the tissue, stretching the cell membranes.
For a long time, the pump was written off as a purely cosmetic effect with no bearing on growth. But research into hypertrophy mechanisms suggests that membrane stretch from fluid influx (so-called cell swelling) can itself act as a growth signal — the cell 'reads' that stretch as a reason to reinforce its structure to handle similar pressure in the future.
That doesn't mean you should train purely for the pump — heavy, low-rep sets remain an important part of building strength and size. But tacking high-rep, short-rest sets onto the end of a workout isn't pointless vanity — it's a genuine extra growth stimulus.