How would a Reformed theologian distinguish his or her view of atonement?

The term 'limited atonement' has been used, and I wonder how the Reformed is differing by definition from the Evangelical view of atonement. Further, what Scriptures do the Reformed base this view upon? (I have attempted to answer some questions Biblically, having been brought up mainly in the Evangelical tradition, to find that my answers are dissatisfying for someone seeking the particular view of the Reformed or Calvinist. I am interested in learning what some specific differences are between the two traditions, having only a general understanding at present. This question is in that vein.)