Here is my translation of a question and answer exchange with Igumen Pakhomy (Bruskov), rector of the Holy Trinity Cathedral in Saratov (Russia):
Question: On Great Thursday Orthodox Christians bring home from the service [of the reading of the Twelve Gospels] burning candles or a lantern with a flame. What is the meaning of this custom? What does one do at home with this candle?
Answer: This is simply a beautiful Russian tradition. Matins for Great Friday is served on Thursday evening, during which the so-called "Twelve Passion Gospels" are read, in which the story of Christ's Passion is related. Parishioners stand with lit candles for the entirety of the service, which they then take home. At home one lights one's icon lamps from these candles. There exists the pious custom of maintaining this Thursday fire in one's icon lamps until Pascha. In olden times the soot from burning Thursday candles was used to draw crosses on doorways.
One should remark, however, that all our external ritual actions, using various objects (lamps, vestments, etc.) are meaningless unless we penetrate their inner significance. From ancient times light, fire, and burning lamps at Divine services have symbolized Christ, Who enlightens our life, our heart. One can put forward as an example the priest bringing out a candle and pronouncing the words "The Light of Christ enlightens all!" at the Liturgy of the Presanctified Gifts. Here the candle is a symbol of Christ, the Light of the world, Who enlightens all who come to Him.
The Thursday fire has a similar symbolic meaning. It is a symbol of the enlightenment of the world with the light of the teaching of the Gospel.