A penis is a part of the body that can be found on a male, but not on a female. It is located between the legs (up the top, right where the two legs join. It juts out the front.) and varies in size from man to man, depending on their age, race, and current temperature. It is a vital part of procreation, and chopping it off is considered to be one of the worst possible things you can do to a man.
Waving it around in public is not considered to be socially acceptable in any country, and is illegal in most.