Because it typically has a man's most excitable erogenous zone, it is an area concentrated on by both him and his sexual partner.
When a male is sexually aroused, the three areas of erectile tissue will usually fill with blood and his penis will expand and stiffen. The penis will often move more upward than in the flaccid (non-erected) state, but the angle varies between males and is no indication of the height of arousal. (A penis can also become erect without the man being aroused.) An erect penis is also known as a phallus and things of that shape, or representing them, can be said to be phallic.
The primary body modification made to the penis is circumcision; during this process, the foreskin is cut away such that the head of the penis is always exposed. A far less common, but popular enough in BDSM and sexually-interested cultures, is piercing of the head of the penis for insertion of a bar or ring.
Because penises vary in size, it is important when buying any device or toy that fits onto the penis to ensure that it will fit without damage. Some toys can do a great deal of harm or, at the least, cause unintentional embarrassment. 
Cock is a vulgar, and some would say, obscene term for penis. It may be approximately as obscene as cunt, but many men are quite happy with calling theirs that (as are some women, vis-a-vis cunt). Some dictionaries say that it is derived from the Old English cocc (rooster), reinforced by Old (and modern) French coq rooster, penis.