Your armpit is the area underneath your upper arm, where it connects to your shoulder. Armpits tend to be smelly, so we would advise to steer clear of an open armpit on a bus or subway.
Another common word for armpit is "underarm," while the official anatomical term is axilla. Perhaps because your armpits tend to get sweaty and a little smelly after you exercise, the word armpit is sometimes used as a derogatory term for an unattractive place: "That city is so ugly it's the armpit of New Jersey." Before armpit, the axilla was known as an arm-hole.