Jamieson, Fausset and Brown on Leviticus 19:28

28. Ye shall not make any cuttings in your flesh for the dead--The practice of making deep gashes on the face and arms and legs, in time of bereavement, was universal among the heathen, and it was deemed a becoming mark of respect for the dead, as well as a sort of propitiatory offering to the deities who presided over death and the grave. The Jews learned this custom in Egypt, and though weaned from it, relapsed in a later and degenerate age into this old superstition (Is 15:2; Jr 16:6; 41:5).

nor print any marks upon you--by tattooing, imprinting figures of flowers, leaves, stars, and other fanciful devices on various parts of their person. The impression was made sometimes by means of a hot iron, sometimes by ink or paint, as is done by the Arab females of the present day and the different castes of the Hindus. It is probable that a strong propensity to adopt such marks in honor of some idol gave occasion to the prohibition in this verse; and they were wisely forbidden, for they were signs of apostasy; and, when once made, they were insuperable obstacles to a return. (See allusions to the practice, Is 44:5; Re 13:17; 14:1).