The penis isn't a muscle. There are muscles around and near it, but none in the penis proper.
WARNING: The following may require a copy of Gray's Anatomy to comprehend.
Jelqing is believed to work in two stages:
The first stage causes the easiest and usually most dramatic gains thoughout a PE career. This stage causes elongation of the pubococcygeal ligament. Like any other ligament, with proper warm-up, you can stretch this ligament. The pubococcygeal ligament is what holds the penis against the pubic bone and is the one severed during so-called lengthening surgery. Stretching it causes the apparent length of the penis to increase because it allows more of the inner penis to move forward and be exposed. You can also strengthen the muscle that connects to that ligament, the pubococcygeal muscle, otherwise known as the PC muscle. This is the muscle you flex when you perform Kegels. Building the PC muscle through kegeling makes for stronger erections and greater ejaculatory control.
You do know that half or more of your penis is internal, right?
So where do the muscles come in? There are two, the ischiocavernous and the bulbocavernous. These muscles wrap around the two chambers inside the penis responsible for erection the corpus cavernosa, and the corpus spongiosum, the spongey tube in the middle that carries the urethra and terminates in the glans penis (the helmet). The corpus does inflate somewhat, but usually not nearly as much as the other two chambers. The ischiocavernous (IC) and bulbocavernous (BC) can be worked, like other muscles, and increased in size. This is the second phase of jelqing. After you get the easy gains from building the PC muscle and stretching the PC ligament, the only way to gain after that is to stretch the IC and BC muscles. Unfortunately, these two muscles are involuntary, meaning you cannot control their movement mentally. No Cybex for the penis anytime soon. What you have to do is work them manually by warming the penis and jelqing. Jelqing breaks-down the muscle fibers in the IC and BC causing them to rebuild themselves when at rest. Just like other muscle exercises, this repeated process of break-down and rebuidling results in gain of muscle mass.
Beneath these two muscles is yet another thingy, the tunica albuginea. The tunica albuginea is really important because it's what keeps your corpus cavernosa and corpus spongiosum from losing their form. Its function can best be imagined by taking a penis pump tube and inserting two long completely compacted sponges. Now add water. What happens is the tube forces the sponges to grow only within the confined space of that tube. The sponges are your corpusi and the tube is the tunica. Getting the IC and BC to grow is good, but for true growth you've got to cause tissue expansion of the tunica and the underlying corpusi.
Yeah, you can do this. You've all seen pictures of various aboriginals who expand body parts causing tissue expansion in those parts through ever-larger decorations. Things like ears, lips, and yes, penises can all be expanded in size by causing constant tension or traction on the tissue. The traction causes new cells to be created and thus your penis can be enlarged. This takes time and constant effort. The guys you see in National Geographic with foot-long penises because they wrap their penises around sticks, don't get strong erections. Jelqing allows the tissue expansion to occur while preserving and even enhancing (through improved blood flow and muscle building) erections.
Jelqing works on length and width though variants can target one or the other. Pumping does work but usually requires more time and effort. It too forces expansion of the tissues of the penis but the best workout likely combines pumping and jelqing.
Warm-up and warm-down are essential to jelqing or pumping properly, just like stretching prior to working out other body parts.
Until genetic therapy allows us to isolate the penis size genes and Jonah sells his genes on the open market, this is the best we've got.