Using the term holiday to describe an extended amount of time that you are taking off from work is perfectly ok. I don't think the employer needs to know every detail about your life when you are absent. Sometimes an extended period of time is needed to get away from the every day work life style, which can be very stressful at times depending on the job you have.
The use of the word "holiday" is a britishism and for that reason it sometimes sounds strange to Americans, but it is perfectly correct. A lot of times, British words and expressions seem dated to Americans but that is just because American English has evolved away from British English and therefore words that were once in use in the United States are not in use anymore. Holiday is a good example of this.