Groundhog Day is a popular, albeit unofficial, holiday in North America. The holiday originated in North American 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.
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.
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)