It comes from the Latin requiescat in pace, which means rest in peace and is a Christian phrase that appears as early as 525 AD as part of the death rituals of the early Church and seemed to exist in conjunction with other Latin Church sentiments attaching the idea of rest or sleep to death—as outlined by Tuker and Malleson. There is some evidence that it’s a formalization of a generalized sentiment rooted in older Jewish culture and religion, but it’s difficult to make any firm connection between the two—though, it wouldn’t be unreasonable to suppose given their shared history.

The meaning of the phrase in its earliest form, according to Leahy, was to signify that the departed died in union with the Church and, by extension, Christ. As time wore on, it came to be a general, Christian expression of the desire for the departed to have peace in the afterlife. Despite being connected to the death rituals of the early Church, it didn’t appear on gravestones until the 8th century. By the 18th, it was ubiquitous, and in the modern day, its use has waned appreciably.

His Mass and Ours: Meditations on Living Eucharistically. Leahy (2012)

Handbook to Christian and Ecclesiastical Rome. Tucker, Malleson (1900)