Imbolc is originally an Irish holiday, celebrating the beginning of spring, and associated with the goddess Brigit, and thus later Saint Brigit.
There may have been a prescendent on the Coligny calendar; the month wherein Imbolc would fall is called Ogronios, possibly meaning "end of the cold". According to Cormac's Glossary, it’s also the feast of the goddess Brigit, patron of poets, smiths, and healers—one of the triple goddesses of Irish mythology, and a goddess of sovereignty who, in her marriage to Bres, stood as a bond between the Fomorians and the Tuatha Dé Danann, her own people. She is also one of the pan-Celtic goddesses of the ancient world, appearing also as Brigantia in Roman Britain, and in place names in Europe and the Isles.
In the Christian era, the time was associated with the feasts of Candlemas and St. Blaise’s Day—both of which involved the use of candles and their flames as blessings. When I was a child in the Catholic Church, February 3rd meant a special Mass that involved being blessed around the throat by crossed candles; in former times, these candles were lit. Meanwhile, Candlemas is associated with the purification of the Virgin Mary after giving birth to Jesus. The connection of Mary and Brigit can also be tied to the idea of Brigit as Jesus’ wet nurse—and so it’s not surprising that Brigit would eventually share her holiday with Mary.
Going further with the idea of purification, I’ve seen research—-I think it was in the journal Ériu—-that the word Imbolc, from Oimlec, may originally refer to purification, possibly through bathing in milk. It does not refer to the lactating of ewes or the birth of lambs, despite the folk etymology. This connection to milk and cows again connects to Saint Brigit, to whom the cow was sacred.
The idea of purification in early February can be tied to other IE cultures, particularly the Roman februum—-the time of purification, which gave its name to February. To have a goddess of healing associated with this holiday is not surprising—-Imbolc is a time of healing, of purifying, of preparations for spring.