I've kinda talked about pumps before, but let's go into a little more detail this time.
Firstly, what is a "pump"? Many individuals can train for months or years before experiencing one. Seasoned lifters can grow so accustomed to them that the pumps themselves go largely unnoticed. But what the hell is it? Mechanically, the "pump" is a profusion of blood in the target muscle caused by the body's natural reaction to muscular contractions. In addition to cleaning up the cell damage caused by catabolism, your body is also constantly replenishing ATP stores in order to power your muscles. This causes a major influx of blood to the target muscle, creating mild congestion, e.g. swelling, slight numbness and tingling, as well as a slightly engorged appearance.
Muscular contractions (such as those performed during weight training) originate as conscious effort from the brain. Basically, an electrical charge innervates the muscle fibers, causing a cascade of effects which ultimately leads to a contraction. Within each innervated muscle fiber are myofibrils surrounded by sarcoplasm--a calcium rich plasma--within each myofibril are thin filaments formed by actin and myosin. The electrical impulse from your brain depolarizes the inner portion of the muscle fiber, activating voltage-gated calcium channels which react with calcium-release channels. These channels react with the sarcoplasmic reticulum (an organelle regulating calcium concentrations in the muscle), allowing the release of calcium, which binds to the actin containing filaments. This in turn allows a modulation of proteins along the actin chain, allowing the previously blocked myosin filaments to bind to the actin filaments. In the absence of calcium, this is not possible. This binding pulls the bands together, resulting in contractile force. Then, ATP (remember this guy?) binds to the myosin, weakening its binding state to actin and thereby releasing it--resulting in a relaxation of the muscle fibers.
So during muscular contractions, your body is required to replenish oxygen and ATP, as well as remove waste--all of which are done through the bloodstream. So why have some people not experienced a "pump"? Muscular contractions are not all equal. The complete activation of all muscle fibers will require more bloodflow than a contraction where only some fibers are activated. In a muscle where overload is not being experienced, there will also be less demand for blood. This is why people who train light or people who don't train well will often go pump-less. Once again, this is why isolation, overload, and proper form are absolutely necessary.
How important is a pump in muscular hypertrophy? There is absolutely no evidence to indicate that muscular pumps in any way correlate directly with growth. Meaning, just because your quads got hella pumped, you may not have initiated hella adaptive response (on a strictly acute basis). Ya feel me? However, muscular pumps are an excellent indicator of isolation and should definitely be sought in each workout, and are highly effective as a long-term benchmarking tool as well. It goes without saying that fully activating each muscle--each fiber--will absolutely net you greater gains. In many cases, this will result in a ridiculous pump as well. In my personal experience, pumps are a thing of practice and effort; recognizing the sensation aids in isolation and also acts as a reminder to continually improve form. I also find that those who do not use a HIT approach will have a harder time getting and maintaining pumps (this was me when I first started).
Additionally, there are some who feel the stretching aspect of a pump to be a desired effect in and of itself. These folks argue that the fascia (the sheath surrounding your muscle) becomes stretched as the muscle becomes more and more pumped, or engorged with blood. This is the basis for Fascia Stretch Training-7 (FST-7). This program involves doing 7 sets per exercise, usually 2-3 sets performed progressively heavier, followed by the remaining sets performed progressively lighter and also in a more rapid succession. Arguably, this maximizes the pump in the target muscle, literally stretching the fascia by packing more and more blood into the muscle. The argued benefit from FST-7 is basically that by stretching the fascia out, you are allowing for additional muscle volume to be present. I've used this in the past as a sort of modified "drop-set," but it's a take-it-with-a-grain-of-salt type thing like everything else.
Muscular pumps can be enhanced by nitric oxide products, i.e. SuperPump, Jack3d, etc. For my review of NO products, read this.