Groundhog Day is a popular, albeit unofficial, holiday in North America. The holiday originated in North America with German immigrants (the "Pennsylvania Dutch"), and it is has European roots. It revolves around the superstition that a large rodent of the family Sciuridae is capable of predicting the weather.
The basic idea is that on February 2, people gather around to watch a groundhog with a stupid, alliterative name ("Punxsutawney Phil" in Pennsylvania) come out of its hole. According to legend, if the groundhog doesn't see its shadow (if it's cloudy, or the groundhog is nearsighted), an early spring will come. If it's a sunny day or the lights from the TV cameras are too bright, it sees its shadow, retreats into its home and six more weeks of winter will follow. Some people believe that this is actually an accurate form of weather forecasting. Research in 2012 found that the groundhog was only correct in 4 out of 13 years examined.
It apparently derives from older, European superstition, that a clear day on Candlemas (February 2) means a long winter is in store. Reputedly, Germans used a badger or even a bear in areas where groundhogs were not known. As well as being Candlemas (which commemorates the presentation of Jesus at the temple, when the priest held him up and predicted 6 more weeks of winter), the date is also linked with the ancient pagan festival of Imbolc, traditionally February 1. German weather lore has it that "Wenn sich der Dachs zu Lichtmeß sonnt, so gehet er wieder auf vier Wochen in sein Loch." ("If the badger is in the sun at Candlemas, he will have to go back into his hole for another four weeks.")
The "six more weeks of winter" legend is particularly good for identifying people who are bad at math and/or dates. Exactly six weeks (42 days) after February 2 is March 16 (March 15 in leap years)...only a few days before the vernal equinox (i.e., the end of winter).
Of course, if you're in the Southern Hemisphere, this is all completely meaningless.
In February 2015, a groundhog in Wisconsin decided it was fed up of the attention and bit a local dignitary attempting to solicit weather information.
Groundhog Day is also a 1993 fantasy-comedy film starring Bill Murray as Phil Connors, a Pittsburgh weatherman who is forced to relive the same day over and over, specifically, Groundhog Day. The character uses this miracle as an aid to seducing women, which is very sensible of him, although it's a bit of a downer that he ended up with Andie MacDowell instead of Marita Geraghty. The term "Groundhog Day" has since been used to describe the effect of reliving the same moment repeatedly which is often used in science fiction as a plot device. It is a rather good film, and well worth watching.
A version of this plot, with a few major differences, was first written in 1905 (published in 1915) as The Strange Life of Ivan Osokin by P. D. Ouspensky. In this book a man who repeatedly relives his life is, unlike the Bill Murray character, unable to make significant changes.
"Spring" is a Canadian term, which means "eight more weeks of winter".
- Straight Dope article on Groundhog Day (Spoiler alert: It's not a very good tool for predicting the weather)