Literally: big – peace – joy – day
Alternately: A good day for doing things. Specifically, 大安 was a very auspicious day under the old 陰陽 (Onmyou, Japanese style yin-yang) divination system, and this compound emphasizes this positivity by adding 吉日, “a good day.”
Notes: This one has a lot of different readings. 大 may also be pronounced dai; 吉日 may also be prounounced as kitsunichi or kichinichi. (Kitsujitsu doesn’t seem to be used in this yojijukugo, though.)
If you want to get lost in interesting historical trivia for a while, you can look into the Onmyou system a little more deeply. Vaguely equivalent to the horoscopes we know in the West, it was a shifting cycle under which certain times and directions were thought to harbor good energy, making them auspicious for starting tasks, running errands, making visits. Other times were bad, meaning you should lie low, and sometimes directions became bad, meaning you should avoid them. You see this popping up in things like the Tale of Genji, where the season, day, and even time of day might determine who you visited or whether you stayed at home. But even in 2018 you can find calendars listing auspicious days, or get fortunes at shrines, that reference this system.
Keen observers will notice that Tuesday, November 6th was 先勝 (senshou, although also sometimes pronounced sakikachi or sakigachi) is “lucky in the morning, but not in the afternoon” – i.e. a mixed bag of a day.