What does the wreath represent on the advent wreath?

Roman Catholic AnswerTo the best of my knowledge, there is no assigned meaning to the evergreen, although this is not to say that people don't have things that it represents to them; there is no official meaning.

from Modern Catholic Dictionary by John A. Hardon, S.J. Doubleday & Co., Inc. Garden City, NY 1980

Advent Wreath. A band or circle of green foliage, surrounding four candles that may be enclosed in glass and are lighted successively in the four weeks of the Advent season. They symbolize the coming celebration of Christmas, when Christ the Light of the World was born in Bethlehem. The wreath originated in Germany, and in some countries there is a special ceremony, with prayers and hymns, associated with the lighting of the candles on the Sundays of Advent.

The candles are purple because Advent is a penitential season, but the third one is rose as the theme of the liturgy that Sunday is of joy.