Historically, the Feast of the Presentation of the Lord in the Temple would involve the blessing of candles by the local priest — hence ‘Candlemas’. Also, as we shall see in what I am about to post, people carried their own candles, at least in the twelfth century. And why carry lights? What is the significance of light? Let us remember that Christ is the Light of the World. Here is Cistercian abbot Guerric of Igny (1070-1157), from a sermon for this feast:
But let us rather discuss, if you will, the lovely custom in the Church of bearing liths on this feast-day, and how it bodies forth what was done in the past and also what we should be doing now. Not that I suppose you are unaware of this, even if it has never been set out for you. Which of you today, bearing a lighted candle in his hands, does not instantly call to mind the old man who took Jesus in his arms this day — the Word clothed in flesh as the candle-flame is cupped in wax — declaring him to be the light that would enlighten the Gentiles. And Simeon was himself a lamp lit and shining, bearing witness to the light, he who came at the Spirit’s prompting into the temple, to receive, O God, in the midst of the temple your loving-kindness, and to proclaim him to be indeed your loving-kindness and the light of your people.
Ah! brothers, look where the candle burns in Simeon’s hands; that is the light to light your tapers from, those lamps which the Lord would have you holding. Go to him and you will be lit up, not so much bearers of almps as lamps yourselves, shining within and without, lighting yourselves and your neighbours. May this lamp be in heart and hand and mouth: a lamp in your heart to light yourself, a lamp in your hands and on your lips to light your neighbours. The light in your heart is loving faith; the lamp in your hands is the example of good deeds; the lamp on your lips, helpful and strengthening words. We must not only shine in the sight of men by our deeds and words: we need to shine through prayer in the sight of the angles and before God in sincerity of heart. We light in the sight of the angels the lamp of pure devotion when we sing with diligence and pray with fervour. Our lamp that burns before God is our singleness of heart in pleasing him alone whose approval we have won.
So that you may light all these lamps for yourselves, my brothers, come to the source of light and be enlightened. Draw close to Jesus … (From the First Sermon for the Purification, in The Cistercian World, ed. and trans. P. Matarasso, pp. 133-135)