Here's an excerpt from an article I wrote a few years ago. It doesn't include the discussion of the "stretching bag" theory of muscle growth but it does explain pumps a bit.
The rapid increase in blood flow to your muscles after a set of curls has been attributed to several metabolic or “chemical signals” including adenosine, adrenaline, potassium, lactate, carbon dioxide and nitric oxide.
When a muscle contracts, the pressure of the contracting fibers squeezes all the blood out from the blood vessels permeating the tissue. This causes all the aforementioned chemical signals to be released into the surrounding area of the muscle which ultimately leads to relaxation of blood vessels and a rapid and dramatic increase in blood flow to make up for the oxygen deficit created during contraction. Increasing blood flow to working muscles is not only necessary to remove carbon dioxide and deliver oxygen, but also necessary to counteract the vasoconstricting effects of hormone-like catecholamines (i.e. adrenaline, noradrenaline) released at the onset of intense exercise. The potency of each rep to get a pump going is related to how many fibers are recruited when the muscle contracts. (Hamann, 2004)
From above you’ll recall that when you lift a weight, blood supply is temporarily cut off from the muscle with each contraction. This sends your muscles into metabolic overdrive and you feel a deep burning sensation. When this happens, you get an increase in oxidative byproducts, changes in the ADP/ATP ratio, a temporary drop in pH, and several other indicators that the muscle’s need for oxygen rich blood has dramatically increased. Turns out, these same signals from the cell that lead to a pump also trigger signaling pathways within the muscle cell that will increase “muscle quality”.
Muscle quality is described as the ability of the muscle to endure a metabolic challenge. In other words, your muscle grows better able to withstand the metabolic demands of lifting weights. As our friend Martha would say, it’s a good thing!
I think that there is one more benefit of getting a good pump in your muscles when you train, motivation. There are few things more motivating that seeing your muscles grow before your very eyes. Veins popping, skin tightening with every rep, its arguably one of the greatest things about lifting weights. If that’s what it takes to keep you on track with your training, then it’s a critical part of the whole training experience.
References:
Hamann JJ, Buckwalter JB, Clifford PS, Shoemaker JK. Is the blood flow response to contraction determined by work performed? J Appl Physiol. 2004 Feb 6
Bhasin S, Woodhouse L, Casaburi R, Singh AB, Bhasin D, Berman N, Chen X,
Yarasheski KE, Magliano L, Dzekov C, Dzekov J, Bross R, Phillips J, Sinha-Hikim
I, Shen R, Storer TW. Testosterone dose-response relationships in healthy young men.
Am J Physiol Endocrinol Metab. 2001 Dec;281(6):E1172-81.
Lee SJ, McPherron AC. Myostatin and the control of skeletal muscle mass. Curr Opin Genet Dev. 1999 Oct;9(5):604-7.