Your penis comprises three tubes, basically: one on each side and one on the bottom, which contains the urethra and attaches to the glans, or head of the penis. (You can find diagrams in the library in a good book on human anatomy.)
Those tubes fill up with blood during an erection, and expand. How much they expand differs from person to person. With most men, the penis is smaller while flaccid and gets much larger when erect. A minority have penises roughly the same size flaccid and erect. They just get hard during an erection. Some people refer to "growers" and "show-ers."
The two tubes on the sides (corpora cavernosa; singular corpus) are covered with fascia which attaches to suspensory ligaments, which in turn attach to the abdomen or the pubic bone. When you feel a little bumpiness under the skin about halfway down your penis shaft, you're probably feeling the ligaments where they attach.
Alongside the dorsal vein on the top of the penis runs the dorsal nerve. The main problem with loop attachment devices (Ironman, JES Extender, Peni-Stretcher, Max Xtender etc) is that they tend to put the most pressure on the top of the penis, where there's the most chance of creating problems with vein or nerve.
The spongy tissue of your penis extends inside your body as well (if you've never tried it, play around behind your balls the next time you have an erection).