See Matthew 5:39-40.

Thy cloak - thy coat - In Matthew 5:40, I have said that Coat, χιτωνα, signifies under garment, or strait coat; and Cloak, ἱματιον, means upper garment, or great coat. This interpretation is confirmed by the following observations of Bishop Pearce. The χιτων was a tunica, or vestcoat, over which the Jews and other nations threw an outer coat, or gown, called a cloak, Matthew 5:40, (which is meant by ἱματιον), when they went abroad, or were not at work. Hence the common people at Rome, who did not usually wear, or had no right to wear, the toga, are called by Horace tunicatus popellus, Epist. i. 7, 65. This account of the difference between the χιτων and the ἱματιον appears plainly from what Maximus Tyrius says, The inner garment which is over the body they call χιτωνισκον, and the outer one the ἱματιον. And so Plutarch, (in Nupt. p. 139, ed. Fran. 1620), speaking of a man who felt the heat of the sun too much for him, says that he put off, τον χιτωνα, τῳ ἰματιῳ, his vestcoat also with his cloak.

And unto him that smiteth thee on the one cheek,.... The right cheek,
offer also the other; the left cheek, by turning it to him, that he may smite that likewise, if he thinks fit: by which proverbial expression, Christ teaches patience in bearing injuries and affronts, and not to seek private revenge; but rather, suffer more, than indulge such a temper; and for the same purpose is what follows urged:
and him that taketh away thy cloak, forbid not to take thy coat also: the phrase is inverted in Matthew; See Gill on Matthew 5:39. See Gill on Matthew 5:40.

To him that smiteth thee on the cheek - Taketh away thy cloak - These seem to be proverbial expressions, to signify an invasion of the tenderest points of honour and property. Offer the other - Forbid not thy coat - That is, rather yield to his repeating the affront or injury, than gratify resentment in righting your self; in any method not becoming Christian love. Matthew 5:39.