The concept is much much much older than Christianity. Holidays (Latin fēsta or fēriae) were set aside for the gods in Greco-Roman thought, and it was nefas, religiously incorrect, to perform labor on those days. You can see this concept also in Jewish (ie non-Indo-European) thought, both ancient and modern.

The premise is "the cutting" (Greek temenos), the notion of separation of the divine from the mundane. Greek sanctuaries were clearly marked out spaces with obvious boundaries, and there were strict rules for who or what could pass beyond those boundaries. Pregnant or menstruating women, for instance, were considered unclean and were not permitted to cross the temenos. The same idea is applied to the day of the holiday (or the hour, or the moment): it is cut away, set aside, for the god(s) and should not be polluted with unclean acts. Working a trade is in that category. The Romans were, generally speaking, less strict about such things than the Greeks or other PIE societies, but conversely also observed many more holidays. The Romans had hundreds of festival days. The rich could be expected to observe most of them, more or less, without trouble, but a bricklayer struggling to feed his family would obviously not be able to be idle for half the days of the year. He had to pick and choose.

If we could peer back into the very dimmest, earliest days of PIE/Semitic societies, we no doubt understand that this concept of separation from normal everyday life was fundamentally a community-building concept. On the day sacred to the fertility god, it is the duty of the community as a whole to observe and not to be off chopping wood or doing laundry. Those activities are necessarily problematic on the festival day because they are not participatory in the communal effort to propitiate the target god(s).