A holiday is a special day for religious or cultural reasons - such as Christmas, Easter, New Year's Eve, and your country's Independence Day. Some holidays are also official days off from work, and others are not.
A vacation is when you take multiple days off from work/school to relax and/or travel. However, American English speakers call this a vacation and British English speakers call this a holiday:
My parents are on vacation in Asia. (American English)
My parents are on holiday in Asia. (British English)
In your own backyard, that is. Always wanted to go to Japan? Hit up your local museums Japanese collection, grab sushi at your favorite restaurant, and then sing the high notes at your local karaoke bar.