The feast of St. Barbara is traditionally celebrated on December 4th and still is universally within the calendar of the usus antiquior; it is also still kept on this day within the modern liturgical calendar of the German speaking countries of Europe, where there is yet a great devotion to her.
Various legends surrounding St. Barbara were attached to flowering branches. One is that flowers blossomed upon her grave on Christmas day; another that, imprisoned in a tower awaiting martyrdom, St. Barbara found a dried up cherry tree branch which she watered and which bloomed, thus bringing her consolation before her martyrdom.
The custom thereby arose that, each year on her feast, people would go out and cut some branches from some flowering wood such as a cherry, hazel, forthysia or apple, prepare them, place them in a vase indoors, watering them. This done, people would wait in expectation for them to blossom on or around Christmas Day -- which accordingly ties in very nicely to Advent and the expectation of the birth of Christ.
Barbara's Branches
(Thanks to Gregor for filling in a number of details.)
