Burning of votive candles

Why do we have candles burning in the back of the church by icons and statues?

First it is important to remember that the Church practices use many rich signs and symbols. Rather than rewrite what someone else has done well, I will defer to Rev. William Saunders. “The History of Votive Candles” from Arlington Catholic Herald in 2003. [I believe the specific link is no longer active]

Before addressing the use of votive candles in particular, we have to appreciate the symbolism of light and the general usage of candles in religious practice. In Judaism, a perpetual light was kept burning in the Temple and the synagogues not only to insure the ability to light other candles or oil lamps in the evening but also to show the presence of God (cf. Ex 27:20-21 and Lv 24:2-4). Later, the Talmud prescribed a lit lamp at the Ark, where the Torah and other writings of Sacred Scripture were kept, to show reverence to the Word of God. (This practice probably influenced our own tradition of having a lit candle near the Tabernacle to indicate the presence of and to show reverence for the Blessed Sacrament.)

Here, as in early Christian times, we light a candle before a statue or sacred image of our Lord or of a saint. Of course, we do not honor the statue or the image itself, but whom that statue or image represents. The light signifies our prayer offered in faith coming into the light of God. With the light of faith, we petition our Lord in prayer, or petition the saint to pray with us and for us to the Lord. The light also shows a special reverence and our desire to remain present to the Lord in prayer even though we may depart and go about our daily business.
Original source – http://www.catholiceducation.org