Final answer:
The 7-letter word for a day off that originally referred to a religious observance is 'holiday', derived from the Old English for 'holy day'.
Step-by-step explanation:
The 7-letter word for a day off from school or work that originally referred to a religious observance is holiday. This term originates from the concept of a holy day, which is a day set aside for special religious significance. The practice of taking holidays can be traced back to religious traditions and observances, where days were allocated for rest and worship. Over time, the term holiday has evolved to include any day of exemption from work or school, not necessarily connected with religious practices. However, its roots are clearly in religious observance, as indicated by the etymology of the word from the Old English hāligdæg, which literally means 'holy day'.