A day of excitement or a circumstance of opportunity.
The origin use of this term comes from the military. The literal sense of the term, i.e. a day spent in field manoeuvers, is now little used. The first reference we have for that meaning is from 1747, in Scheme Equip. Men of War:
"These periodical Intervals of eating and drinking ... are to the Citizens as it were Field Days, for improving their Valour."
A more specifically military reference comes from a little later, in The Edinburgh Advertiser, May 1776:
"The officers, on a general field day, instead of commanding, are obliged to coax them [the soldiery] to go through their different manoeuvers."
'Field day' was a commonly used term in the military throughout the rest of the 18th century. During the 19th century it began to be extended to refer to any event that might happen in a field; for example:
Hunting: "Sometimes a dance (though rarely on field days, For then the gentlemen were rather tired)." - Lord Byron, Don Juan, 1823.
Scientific expeditions: "We had a delightful field-day in the abbey." - Sir George Gilbert Scott Recollections, 1878.
Around that time the term also began to be used for any exciting or welcome event, as in Thomas Creevey's Letters, 1827:
"Saturday was a considerable field day in Arlington Street, ... and a very merry jolly dinner and evening we had."
We spend less time in fields now than before and during the 20th century the term was further extended to include opportunity as well as enjoyment; for example, 'Clergyman found drunk in nightclub - the tabloids will have a field day with that'.