Why on this year (and on other years that precede civil leap years) do we start praying for rain in the Diaspora (by inserting the phrase 'Vetein tal umatar") at maariv of December 5 and not maariv of December 4 like most years?
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The Jewish day starts at night, but V'sein Tal Umatar is based on solar calendar, so it can sometimes be a day later. Plus the date was established in Julian Calendar, so there's also the Julian->Gregorian shift to keep us busy...
The Gemara (Taanis 10a) says that in Bavel we start saying V'sein Tal Umatar on the 60th day after Tekufas Tishrei - the autumnal equinox (why is beyond the scope of this question). This is followed in all of Chutz Laaretz (here too, why is beyond the scope of this question).
[note: for purposes of this calculation we use the astronomically-imprecise Tekufa D'Shmuel to approximate the autumnal equinox]
With that being said, we need to figure out when the "autumnal equinox" is, so we can add 60 days.
Because the equinox follows the sun, we will need to look at the solar calendar. As you may know, the modern-day Gregorian Calendar was not always used. At one point in time, the Julian Calendar (with slightly different rules) was the norm. The Halacha to say V'sein Tal Umatar was established when the Julian Calendar was in use, so the date chosen was: November 21 or 22 in the Julian Calendar.
Why can it possibly fall out on two different days? Let's take a look at a sample 5 years to develop a simple pattern:
See it now? In each year after 2008, the Tekufah has a 6-hour drift. But the drift resets because we know every 4 years has a leap year (or at least that's how it was in the Julian Calendar).
But... one of those years is a "problem". We know that the Jewish day starts out at night. So if the Tekufah falls out on October 7th at 9:00 pm [as it does in the 4th bullet] we will need to count it for the next day. So, as you can see we emerge with: in the year before a leap year, we knock the day forward 1.
Fast forward to today's times where we use the Gregorian Calendar. We need to translate that date into the Gregorian Calendar. To do so, we need to keep in mind all the subtleties of differences between the two. As time goes on the two calendars (ever so slightly) drift further and further apart [the first drift occurred immediately, when 10 days were "erased" from the calendar].
Putting it all together
This year (2011) is the year before a leap year. It also happens to be that we are running a 13 day difference between Julian and Gregorian. So take November 22, add 13 days, and voila: December 5, 2011 emerges.
And going forward
The next time the Julian and Gregorian calendar fall out of step will be in 2100. We'll worry about it then...