In the evening of Christmas Eve a log cut from a tree, the Yule log (badnjak), is placed on the fire. This young tree, usually oak, symbolizes Christ and his entry into the world. Burning of the Yule log presents the warmth of Christ's love. Then, Christmas Eve is a reminder of the tree that the shepherds brought into the cave and which the righteous Joseph burn to warm the just born God-child in the cold cave.
There is another interpretation: Christmas Eve is a hint of the suffering of Christ and His Cross. The straw that is brought into the house is a reminder of one straw from the crib on which the Most Holy Mother of God placed the just born Lord. The frankincense which is used to cense the house, as well as the gifts that are placed in the straw, are the reminders of the gifts that the wise men from the East brought and gave to Newborn Christ.
Source: Diocese of Zvornik and Tuzla