The Christ Candle represents the light that the Son brought into the world when he was born a little baby, God in the flesh. This was the very light of God, come into the world:

In him was life, and the life was the light of men. The light shines in the darkness, and the darkness has not overcome it (John 1:4-5).

On Christmas Day and the Christmas Sundays, the Advent candles are usually removed, but the Christ Candle remains. This reminds us that old things have passed away, all has been made new, and Christ gives his light to everyone:

The true light, which gives light to everyone, was coming into the world (John 1:9).