Field day is a part of the phrase "have a field day". It is an idiom in the English and its origins can be traced back to military terms. Thus it is derived from the military use. It denoted a day of parade in the military parlance. A parade is considered to be much easier than the usual drilling and forced exercise. Since then this phrase has evolved and in the modern times it is a phrase that expresses the act of having a great time or having a great deal to do.

Thus it is an informal expression for a time of great pleasure, activity or opportunity. This term has been in English language since the 1700s but was used as a colloquial term by the military and was later also used to indicate a day set apart for sports and games i.e. a day for physical activity and athletic pursuits. But it gained its current meaning and denotation only since the 1800s.