The use of Holly began as Christians sought to turn from the pagan use of mistletoe (which symbolizes fertility). As an evergreen, it reminds us of eternal life in Christ. The red berries remind us of the blood of Christ spilled for us. The thorny leaves remind us of the crown of thorns placed on the head of Jesus before his crucifixion. Therefore it reminds us once again of the gift of Jesus to us, his sacrifice on the cross which brings us salvation and eternal life in his presence.
And they clothed him in a purple cloak, and plaiting a crown of thorns they put it on him.
I would also suggest that it can remind us of the parable of the sower.
A sower went out to sow his seed; and as he sowed, some fell [...] among thorns; and the thorns grew with it and choked it.
Luke 8:5, 7
And as for what fell among the thorns, they are those who hear, but as they go on their way they are choked by the cares and riches and pleasures of life, and their fruit does not mature. And as for that in the good soil, they are those who, hearing the word, hold it fast in an honest and good heart, and bring forth fruit with patience.
Luke 8: 14, 15
During the busy Christmas Season, let us not get so wrapped up in buying gifts, decorating our homes, baking cookies, attending parties and all the other demands of the season, that we lose our focus on the true reason we celebrate in the first place.