Symbolism
It is common to say a small prayer whilst lighting a candle. As Eliza explained, praying creates a moment of contact between yourself and God. Although not lighting a candle does not make this point of contact weaker, lighting a candle can bring an extra layer to the prayer. It is not only the habit or tradition that creates this extra power: lighting a candle adds a material aspect to the prayer. It creates a physical representation of the prayer. Moreover, the candles burn for much longer than a prayer can last. One could say that, in a way, the prayer continues as long as the candle burns. Whilst you continue your day, the candle and the thoughts behind it can remain with God. This is a thought that might touch the essence of why the burning candle is such a powerful symbol.
Burning candles have many other meanings as well. In the Christian tradition candles, and the light they stand for, have been used to express power, faith, love, honesty and doing good. Furthermore, God and Jesus themselves have been portrayed as manifestations of light many times. [For instance: Christ called himself the Light of the World in several verses, (John 8:12, 9:5; 12:46) and during the Transfiguration of Jesus "his face lit up like the Sun." (Matthew 17:2)] In addition, burning candles have played a major role in funeral practices, thereby functioning as a connection between heaven and earth.