If you're a Catholic, you're probably familiar with the phrase by now. In this Zenit article, Father Cantalamessa gives a readable account of the whys and wherefors of the new evangelization called for by Pope Benedict. This article is actually the fourth in a series of Advent reflections which I only followed sketchily, but since this one helps put the others in better context, it will be worthwhile to read the others as well.
The previous evangelizations pertained to the Graeco-Roman world, the barbarian world and the new world. The current wave, says Father Cantalamessa (and the Pope, of course), is directed "to the western world that has been secularized and in some respects is post-Christian. This analysis, which already appeared in the writings of Blessed John Paul II, has become explicit in the teaching of the Holy Father Benedict XVI."
Fr. Cantalamessa says that the western world is characterized by "scientism, secularism, and rationalism -- the three mindsets that lead to a common result, relativism."
I've only highlighted a few opening paragraphs of the article.