Like so many words that joined the language in the Middle English period, vacation comes from Anglo-French, the particular kind of French spoken in medieval England, and ultimately from Latin: vacātiōn-, vacātiō means "exemption from service, respite from work," and traces back to vacāre, "to be empty, be free, have leisure."

Like vacation, vacate is ultimately from vacāre, which along with meaning "to be empty, be free, have leisure" also means "to annul."

https://www.merriam-webster.com/wordplay/vacation-definition-history