Cupid's bow is a facial feature where the double curve of a human upper lip

Lip

Lips are a visible body part at the mouth of humans and many animals. Lips are soft, movable, and serve as the opening for food intake and in the articulation of sound and speech...

 is said to resemble the bow

Bow (weapon)

The bow and arrow is a projectile weapon system that predates recorded history and is common to most cultures.-Description:A bow is a flexible arc that shoots aerodynamic projectiles by means of elastic energy. Essentially, the bow is a form of spring powered by a string or cord...

 of Cupid

Cupid

In Roman mythology, Cupid is the god of desire, affection and erotic love. He is the son of the goddess Venus and the god Mars. His Greek counterpart is Eros...

, the Roman god of erotic love. The peaks of the bow coincide with the philtral columns

Philtrum

The philtrum , is a medial cleft common to many mammals, extending from the nose to the upper lip, and, together with a glandular rhinarium and slit-like nostrils, is believed to constitute the primitive condition for mammals in general...

giving a prominent bow appearance to the lip.

The phrase is common in literature, often used related to speech, and therefore the mouth, as in Shakespeare's "Venus and Adonis":

For pity now she can no more detain him; (577)

The poor fool prays her that he may depart:

She is resolv'd no longer to restrain him,

Bids him farewell, and look well to her heart, (580)

The which, by Cupid's bow she doth protest.