A holiday began as a holy day.
Holiday descends through Middle English from Old English hāligdæg. The compound joins holy and day. Modern uses include secular days off and, especially in British English, a vacation, so the name now reaches beyond religious observance.
The selected stages omit Middle English; the descent described above includes it.
Source
Merriam-Webster: holidayWord History gives both components; the definitions cover religious observance, days off and British vacation usage.