And here is the BrE explanation:
A holiday (noun) is a time when you travel away from home for rest and relaxation, either in your own country or abroad, alone or with family and friends. Holidays is the plural.
I have booked a holiday to Italy in August with my boyfriend.
How many holidays are you going on this year?!
Only two. We went to France on holiday in March and then it's Italy in August.
A national holiday (what Dave referred to as recognised/celebrated days) is called a "Bank Holiday". Normally they fall on a Monday but over Christmas and Easter they can be other days of the week.
The two-week (approximate) period over Christmas is sometimes referred to as "the Christmas Holiday" or the "Christmas and New Year Holiday" because most people take leave from their job over that time.
The periods when children don't have to attend school are referred to as the school holidays. The Easter holiday is normally about 10 days long, the summer holiday is about six weeks long and the Christmas holiday is about two weeks.
We don't use the word "vacation".