Imbolc, sometimes also spelled Imbolg (pronounced similar to i-molk and i-molg respectively) is a Gaelic or Celtic festival. Traditionally it marks the beginning of spring in the Celtic calendar, though the weather may suggest that winter is still at hand. The corresponding calendar date for the holiday in modern times is February 1st, Saint Brigid's Day. However, Imbolc should not (but still often is) be confused with Candlemas (February 2nd).
History of Imbolc
Celebrations of Imbolc will begin at nightfall on January 31st, this is because of the Celtic tradition that believed days began with the night rather than with sunrise.
The date also places Imbolc (roughly) halfway between the important winter solstice and the spring equinox which were both other special days in the ancient calendars. Imbolc is one of the four Gaelic or Celtic festivals not directly connected to the solstices and equinoxes, but to the change of the seasons - the others are Bealtaine, Lughnasadh, and Samhain. The origin of the feast and the concrete associations to the Celtic mythology are obscure, though a connection to the goddess Brigid or Brigantia (which, again, may or may not have directly evolved into the saint) is widely assumed.
The Irish word imbolc most likely derives from "i mbolg" (Old Irish, roughly "in the belly", referring to pregnant livestock). Another word for the feast, especially popular in neo-Pagan context, is Oimelc (translating as "ewe's milk"). Note that both these would refer to ewes in lamb and the context of the agricultural year - while another theory naming Imbolc as coming from "imb-folc" (which is supposed to mean "a thorough wash") sounds a bit less believable.
Imbolc might have been an important feast in Ireland in the Neolithic period - while we have no proof of this, the alignment of some ancient monuments seems to point that way, literally. The passage into Mound of the Hostages, part of the "sacred landscape" at the Hill of Tara and may be the best-known example, is aligned with the rising sun on Imbolc.
It is difficult to find any reliable records that would point to the exact prehistoric Imbolc customs that were used to mark the Celtic festival. The best that we can do is to look at the customs that have been carried forward into modern times to try and figure out the history from there. The best indicator of Imbolc's historic celebrations are probably the Irish folk customs that are practiced on Saint Brigid's Day.
Generally speaking, Imbolc would have marked the beginning of spring - or at least a time when the worst of winter was over, with days becoming noticeably longer and the sun stronger. The agricultural association with lambing season is obvious, even though there is a window of up to four weeks for this (Imbolc marking roughly the middle of this window, thus making the feast a good and logical indicator). And while nature reawakens (blackthorn is traditionally expected to start blooming at Imbolc), it is also time for a thorough spring cleaning in the house and on the farm.
Weather Lore at Imbolc
As to better weather - Imbolc was also used as a marker for weather-lore much in the way that America's Ground Hog Day is still used. One legend might have people observing Loughcrew or Sliabh na Cailligh ("The Hill of the Witch") closely: it is said that the witch (or the "crone", the third aspect of the "triple goddess") will decide whether she needs to gather more firewood on this day. If she does, the winter will continue for quite a bit with low temperatures. And as she is not the fleetest of foot, the crone will make Imbolc a bright, sunny, dry day to ease the gathering of firewood.
Hence the saying that if Imbolc is a mucky, wet day, winter will soon be over ... and if it is a brilliant day, buy more fuel and warm underwear.
Groundhog Day has the same rule and is celebrated the day after Imbolc. On Candlemas, when in both England and Scotland a bad day heralds the end of winter too.