That's a good question. After I came to Christ, my mother and I became part of a very conservative and legalistic church. In this congregation you didn't borrow liturgical traditions from the past. In fact, we never even used the word "advent" at Christmas time or ever lit a candle in a worship service; that would be too much like the practice of Roman Catholics, even though nobody would ever remotely equate our fundamentalist church with Catholicism. Now you know why I had never even heard of an "advent wreath" until coming into the world of Presbyterianism. Maybe some of you had a similar background. Nevertheless, we haven't answered the title question.
The word "advent" simply means "the arrival of something important or awaited." As each candle of the advent wreath is lit, its light reminds us of the "light of the world," whose birth was foretold long ages before He finally arrived as the incarnate Messiah. This first coming accomplished all that was necessary for our salvation both in His perfectly keeping the law of God, as well as dying to pay the penalty that the law demands for those who violate God's word (as Adam and Eve did at the beginning of humankind.) "God made him who had no sin to be sin {or be a sin offering} for us, so that in him we might become the righteousness of God" (2 Corinthians 5:21). The core of Christmas is to be found in this verse along with John 3:16 and similar passages. Jesus first came as the Servant-Redeemer. He came not to be served, but to serve and give His life as a ransom for many (Matthew 20:28).
As a candle is lit each Sunday of Advent, we are also to be reminded that we await with great anticipation the return of our Savior and Lord. It was this same Jesus who was taken up into heaven and while his disciples watched the heavens engulf their beloved Immanuel an angel said to them, "Men of Galilee...why do you stand here looking into the sky? This same Jesus, who has been taken from you into heaven, will come back in the same way you have seen him go into heaven." (Acts 1:11) He will come back and what a glorious day that will be. The Advent candles remind us that the "light of the world" is destined to make a round trip. He will come again. This could be our last Christmas as we know it.
But what shall we do as we await His second advent? We are to be about the same thing that the disciples were told by Jesus to do. What's that? That is what you find recorded in Acts 1:8, "But you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth." The time between His first and His second coming is a time of witness. It's a time of telling others who Jesus is, what He has done, how He has changed your life and a time to invite others to trust in Christ alone as their only hope of salvation and eternal life in heaven. It's a time to proclaim to everyone we know that Jesus is "the way, the truth and the life" and that "no man comes to the Father but through Him." He alone is the light of the world. The Advent candles of Christmas speak of that glorious truth. May you think on these things each Sunday as we await His second advent which will come as surely as did His first coming. Even so, Lord Jesus, come quickly. Amen.