What is the X in X-mas?
late 14c., from Late Latin propitiationem (nominative propitiatio) "an atonement," noun of action from past participle stem of Latin propitiare "appease, propitiate," from propitius "favorable, gracious, kind, well-disposed," from pro- "forward" (see pro-) + stem related to petere "to make for, go to; seek, strive after; ask for, beg, beseech, request" (see petition (n.)).
The sense in Latin is perhaps because the word originally was religious, literally "a falling or rushing toward," hence "eager," and, of the gods, "well-disposed." Earliest recorded form of the word in English is propitiatorium "the mercy seat, place of atonement" (c.1200), translating Greek hilasterion.
that by which God is rendered propitious, i.e., by which it becomes consistent with his character and government to pardon and bless the sinner. The propitiation does not procure his love or make him loving; it only renders it consistent for him to execise his love towards sinners. In Rom. 3:25 and Heb. 9:5 (A.V., "mercy-seat") the Greek word _hilasterion_ is used. It is the word employed by the LXX. translators in Ex. 25:17 and elsewhere as the equivalent for the Hebrew _kapporeth_, which means "covering," and is used of the lid of the ark of the covenant (Ex. 25:21; 30:6). This Greek word (hilasterion) came to denote not only the mercy-seat or lid of the ark, but also propitation or reconciliation by blood. On the great day of atonement the high priest carried the blood of the sacrifice he offered for all the people within the veil and sprinkled with it the "mercy-seat," and so made propitiation. In 1 John 2:2; 4:10, Christ is called the "propitiation for our sins." Here a different Greek word is used (hilasmos). Christ is "the propitiation," because by his becoming our substitute and assuming our obligations he expiated our guilt, covered it, by the vicarious punishment which he endured. (Comp. Heb. 2:17, where the expression "make reconciliation" of the A.V. is more correctly in the R.V. "make propitiation.")