The Doomsday Rule is a formula that let's you calculate the day of the week of any date in past or future history based on a (relatively) easy math formula plus some simple memorization.
We already know from experience that St. Patrick's Day and Cinco de Mayo always fall on the same weekday. This uses the same general concept.
In a nutshell:
By coincidence of the calendar, 4/4, 6/6, 8/8, 10/10 and 12/12 are always on the exact same day of the week each year. This is called "Doomsday." (And to get a touch fancier, the July 4th and Halloween also always fall on doomsday, as do the palindromic pairs of 7/11 & 11/7 and 9/5 & 5/9). If you know the day of the week the doomsday is for a given year, you can use that as an easy reference points to compare to other days.
2. Anchor Days
Every century has an "anchor day" to use as a starting point. The anchor for the 1900s is Wednesday and for the 2000s is Tuesday. For all practical uses that's all you have to memorize, though history buffs and time travelers may want to learn a few more.
Once you know the anchor, this formula will give you doomsday for a given year:
Last 2 digits of year + last 2 digits divided by 4 (you can discard the remainder) = # of days to add to the anchor.
So if we take November 5, 1955 as an example:
Anchor for the 1900s is Wednesday
55 + 55/4 = 55 + 13 = 68 days after Wednesday.
68/7 is 9 with a remainder of 5 (or to user fancier math: 68 mod 7 = 5)
So Doomsday is 5 days after Wednesday, aka Monday.
11/7 is a doomsday, so 11/5 is two days earlier on Saturday.
Pretty cool, eh?
Even better: The inventor is guy named John Conway.
Wikipedia - Doomsday Rule