The answer
Candles are naturally for giving light. They were used in the past because they gave a soft, subdued light, and because this light inspired humility and awe to a greater extent than brighter, more glaring lights. This explains why we find churches which are lit by candles alone are more awe-inspiring.
They are used nowadays, although we have electric lights, in those special situations when we feel that the people need to concentrate specifically on the light.
They are used, for example, during the reading of the gospel, because we are seeking enlightenment from it, for the Bible says: "Your word is a lamp to my feet and a light for my path. " (Ps. 119:105), and also; " The commandment of the LORD is pure, enlightening the eyes;" (Ps. 19:8).
Candles are also placed before the icons of the saints, as an indication that a particular saint was a light to the world, and that like a candle he or she faded away in order to give light to others. And since the candle requires oil to burn, and oil symbolises the Holy Spirit, so the light of the candle suggests that the saint was not himself giving out light, but this was effected by the grace of the Holy Spirit within him.
We also light candles as a reminder of the presence of the angels, who are also lights and a fire that burns'. And there are two candlesticks which are placed on the altar as a reference to the two angels who are mentioned in the story of the Resurrection.
We light candles at particular moments during the divine Mass, especially during the prayers for sanctifying the sacraments, as a reminder of the presence of God Himself, who is the "True Light "who has come into the world to give light to all people. His advent meant the coming of light to the world.
When the deacons hold the candles in their hands, they are suggesting that the ministers of the church are bearing light to the world for divine guidance. They are to be seen as the torchbearers giving light just as the angels of God give light in heaven.
Candles in general suggest light, and suggest the life of devotion that God wants for mankind. The Bible likens goodness to light, and evil to darkness. The righteous are called the 'children of light', and the wicked the 'sons of darkness'. The Lord said: " Walk while you have the light, lest
darkness overtake you; he who walks in darkness does not know where he is going." (John 12:35)
Light also indicates the transfiguration of the righteous as happened to Moses and Elijah on Mount Tabor and suggests the luminous bodies in which we will be raised in eternity.
The deacons carrying the candles behind the priest, or around him, remind us of the five wise maidens who carried their lamps with enough oil, as a reminder that we should always be prepared.
I wish that I could give you a whole book about the function of candles and lamps in church, as a subject on its own, and not just an answer to one question.
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Thrice-Blessed Pope Shenouda III of Blessed Memory