A light copy edit focuses on correcting obvious grammar and punctuation errors and making the text conform to AP or house style. It is basically the same as proofreading.
A medium copy edit does the same as the light copy edit, plus revises poorly phrased sentences and improves word choices. Organization and flow is improved by rewording and/or inserting headings and subheadings. Also called a line edit.
A content edit incorporates the conceptual level of the writing as well as the mechanics of the medium copy edit. Suggestions are made to provide more context where needed. Reorganizing or rewriting some sections and/or adding transitions can improve the readability and overall flow.