We use the singular holiday in a short period of, say, one or two days.

• We've got a holiday next Tuesday.
• We get five days' Christmas holiday this year.
  

We often use holidays for the 'big holiday' of the year.

• Where are you going for your summer holiday(s)?
  

We always use the singular in the expression on holiday. (Note the preposition.)

• I met her on holiday in Norway. (NOT . . . in holidays . . .)
  

Americans use the word vacation for a long holiday.