The letters ATBASH are an acronym for the first and last letters of the Hebrew alphabet AT = aleph/tav BASH = bes/shim, and ATBASH is a way of predicting when Jewish holidays will fall, based on Pasover
It works like this:
The first day of Passover (alef) and Tisha B'av (tav) always fall on the same day of the week.
The second day of Passover (bes) is always on the same day of the week as the following Shavuot (shin)
The third day of Passover (gimmel) comes out on the same day of the week as Rosh Hashana (resh)
With me so far?
Ok, the fourth day of Passover (daled) always falls on the same day of the week as Simchas Torah. This connection is a bit of a stretch, but daled corresponds to kuf, which is the first letter of the word Kriah "reading." Simchat Torah, of course, is when the reading cycle begins again.
Now it gets a little better
The fifth day of Passover (hay) corresponds to the day of the week that Yom Kippur falls. Yom Kippur is a Tzom, which is how we tie in the letter tzaddi.
Day six (vav) and Purim (pay) are always on the same day of the week
And, guess what? Day seven (zayin) and Yom Haazamaut (ayin) also correspond.