The candles burning on the altar represent the non-created Light of the Trinity, for the Lord dwells in an unapproachable light. They also represent the fire of Divinity which destroys our ungodliness and sins. The candles lit before the icons of the Saviour signify that He is the True Light which lighteth every man that cometh into the world (John 1:9); at the same time, He is a Fire which engulfs and revives our souls and bodies.
The candles lit before the icons of the Theotokos are a symbol of the fact that She is the Mother of the Unapproachable Light, and also of Her most pure and burning love for God and Her love for mankind.
The candles lit before icons of saints reflect their ardent love for God for Whose sake they gave up everything that man prizes in life, including their very lives, as did the holy apostles, martyrs and others. These candles also mean that these saints are lamps burning for us and providing light for us by their own saintly living, their virtues and their ardent intercession for us before God through their constant prayers by day and night. The burning candles also stand for our ardent zeal and the sincere sacrifice we make out of reverence and gratitude to them for their solicitude on our behalf before God.
St. John of Kronstadt