The human larynx rests in a frame of cartilage bound by ligaments and muscle. At the front is the thyroid cartilage creating the lump at the front of the neck known as the laryngeal prominence, known commonly as the Adam's apple.
The larynx grows in males during puberty, and as a result the Adam's apple is much more prominent in adult men than in women or pre-pubescent girls or boys. (This growth of the larynx is also the reason for the voice breaking in teenage boys).
Unfortunately for some transsexual women, the Adam's apple can still be prominent. In order to remedy this, a plastic surgery known as a trachea shave is sometimes performed to reduce the size of the Adam's apple.
The etymology of the term is unclear: Webster's 1913 dictionary states that the term "... is so called from a notion that it was caused by the forbidden fruit (an apple) sticking in the throat of our first parent".