It’s a Scots term for the days of mirth and amusement at Christmas. In the Middle Ages it was a period of misrule and revelry, of mock masses and masquerades, of celebration and not a little gluttony, that lasted the whole twelve days of Christmas, through the New Year (or Hogmanay) to Twelfth Night or Uphaliday.
The celebration has since become more sedate, Hogmanay surviving as the main winter festival (at one time, Christmas Day was hardly observed in some parts of Scotland). For much of the twentieth century the phrase seemed to be dying out, but it’s now enjoying a revival.
The Scots writer J M Barrie (of The Admirable Crichton and Peter Pan fame) described it in his book Auld Licht Idylls of 1888 as “the black week of glum debauch that ushered in the year”. If ever there was a description of people taking their pleasures sadly, that was it.
Daft in modern English means silly, foolish or mad, but here it has an older sense — which survives in Scots — of somebody who is thoughtless or giddy in their mirth, so daft-days is an exact translation of the French fêtes de fou.