From Worship Matters: A United Methodist Guide to Worship Work, Vol. II by E. Byron Anderson:
"Jesus said: "I am the light of the world" (John 8:12). The presence of the light reminds us of Jesus' coming into our world and into our lives. The light is carried into the worship service as a symbol of Jesus' coming into the presence of the worshiping community. Many congregations use two candles on the altar to point out that Jesus was both a human being and God. At the end of the service, the light is carried out into the world to show that Jesus Christ is for all people everywhere; The acolyte leaves the worship service at the pastor's direction, carrying out the lighted candlelighter. This symbolizes the light of Jesus Christ going out into the world where believers are to serve."
From The Acolyte's Book by Hoyt Hickman:
"Since ancient times, light and fire have reminded people that God is here with us. When you bring the light (fire) into the place where people are gathering to worship, and when you light the candles, you are reminding the people that God is with us at home, at school, and at work, as well as in the worship service; Lighted candles also remind us that Jesus Christ is the Light of the world. Many persons like to think of the two candles on or beside the Lord's table as reminders that Christ is both human and divine."
To be sure, the symbolic value of candles is something that developed over time. Oil lamps, and later, candles, were initially used simply to provide light in worship spaces that could sometimes be rather dark so that the presider and others leading worship could see the text or music they needed to read, pray, chant or sing. Check out this video from Liturgy Man.
This content was produced by Ask The UMC, a ministry of United Methodist Communications.