What does have a field day mean?

Answer 1

Field day originated with the military, speaking of a day that they spent in the field doing training and exercises. The first record of it being used to mean a day of frivolity was in 1827 in Thomas Creevey's Letters.

Answer 2

A field day at school means that you get to go outside, eat a picnic lunch, and play games.

The idiom "to have a field day" means that you're really enjoying something -- it could be used both when someone is having some good, harmless fun -- or when someone is having fun at the expense of someone else. You might hear this used when a celebrity does something embarrassing and someone says "The press is going to have a field day with this!" meaning that the newspapers and TV will really enjoy making fun of the celebrity -- probably a little too much fun!