The pump is when the muscle is engorged with blood. So we've got a situation where more blood is flowing into the muscle than blood is flowing out. Resulting in an increase of pressure and volume of the tissue.
Typically the pump is achieved best by trapping the blood within the muscle by using many reps and a rep range that doesn't allow the muscle to relax. This means that the outflow of blood is blocked. We are trapping deoxygenated blood, as well as anaerobic byproducts, ie. acid in our muscles. This explains why the pump burns. Extra nutrients too? interesting, the blood involved in the pump is the same blood that was flowing through the muscle anyways, since it already entered the muscle. We are disturbing the rate of blood flow. This will increase the contact time of the blood/nutrients with the cells. More time means more reaction, more absorption. However as the pump increases, we are slowing the rate of inflow, which means less new blood going through.
The inflow of blood, is about pressure. If the pressure of the inflow of blood is greater than the internal pressure of the "pumped" muscle more blood will enter the muscle, increasing the pump. Once the pressure become equal, blood will no longer be entering the muscle. Do people actually reach this point? I have no idea.
Is this a good thing or a bad thing? I don't think anyone really knows. There are just too many variable to consider. The quality of the pump you achieve isn't going to make or break your progress or results. Get the diet right and train hard, consistently, focusing on progression and everything else falls into place.
The time we're holding the contraction, vs the time the blood is normally flowing throughout the muscle in a day makes it seem inconsequential.
The biggest benefit of the pump is the psychological benefits. You actually see your muscles bigger. This is instantaneous results. You feel good about it. It's like walking around with a hard on for everyone to see. That's why arnold would sprint out of the gym towards the beach. This is reason alone to work the pump.
Cable Curls superset with Cable Overhead tri extension. High rep drop sets. 8,8,8,8, 4x - seems to work best for me. But maintaining contraction and an ass load of reps is what matters.