The heart pumps blood via a mechanical pumping action. So you've got the heart pumping blood through your arteries, then into your arterioles, which divide into even smaller vessels called capillaries. So up until the capillaries, you've got the heart pumping the blood with some force. After the blood goes through your capillaries, delivering oxygen, nutrients, and picking up wastes, they collect into blood vessels called venules, and then those collect into your larger veins. Now while the heart is forcefully pumping blood into the first set of blood vessels (arteries to arterioles to capillaries), there is no equal force that takes the blood back to your heart through your veins; there are other mechanisms that do this: pressure created in your thoracic cavity from breathing, contractions of muscles themselves that push and squeeze the blood back to the heart, and gravity. This is why venules and veins have these little flaps that prevent blood back flow and arteries don't. Now in the case of tensing the abs as hard as you can, you're basically increasing the pressure in your thoracic cavity, forcing more blood into an area and allowing it to accumulate. This is why your veins are popping out. It's essentially the same thing as when you see kids hold their breath really hard and make your face blush; you're trapping the blood by an increase in pressure. You're going to make your veins bulge because you're forcing more blood into those veins, but not letting it go anywhere. As soon as you stop the cause of the increased pressure (abs tensing, ect..) the blood is going to be allowed to continue back to the heart via those mechanisms I mentioned earlier. I don't see any long or short term benefit to doing this, especially when you include the risk of straining something (namely the diaphragm).
There's the anatomy lesson for the day!
Now one thing I do like to do after a set is to flex and pose the muscles in the mirror (the posing is essentially a means for different ways of flexing the muscle). This pumps more blood into the muscles so I'm more pumped and ready for the next set. I usually flex everything after a set except for abs, when I do vacuums instead. Plenty-o-bodybuilders practice this. Remember those mechanisms that draw the blood back into the heart? Well, when you're lifting hard and heavy, you're pumping a lot of blood into the muscles you're working and there is no equal force to draw it out, other than what I mentioned and time. This may have been what the OG poster was talking about and I advocate this fo sho. But you
do not want to totally cut off circulation completely at any point. Circulation is good pie.
Also, if you're going to be doing this or something similar, remember to stretch well after your workouts. Muscle fibers have a tendency to shorten after contraction, so it's important to stretch them out again.