According to the Farmers' Almanac, "blue moon" is a term used to describe the second full moon that occurs in the same month. A "blue moon" occurs every 2 1/2 to 3 years in the Gregorian calendar. In spite of the name, the second full moon of the month is not blue in color.
Two full months in one month? Alhamdulillah!
Do two full months in one month affect us as Muslims? The answer is "no," but is seems like there should be a special dua or something for it, lol.
I asked Brother Khalid Shaukat from Moonsighting.com about the "blue moon." He is a great brother, Masha Allah; he responded to my email almost immediately and put up the response on his website (see 7.23).
While you're over at his site, play a few of the games on the menu. "Do NOT Click" is cute, and he has some neat Math Jokes and Puzzles for your New Year's Eve enjoyment!