A copyeditor does a bit more than a proofreader. S(he) not only looks at punctuation and grammar, but also reviews the sentence, paragraph and overall structure. A copyeditor gives spelling suggestions and pays attention to formalities like standardisation of name spelling or terms and verifies the facts and citations.
Main questions in copyediting:
Is the sentence consequential?
Is the style consistent?
Is there a central theme in the article or story?
Is the flow and structure consistent?
What about the wording?
Does the metaphor fit?
Are there verbs or other words that are repetitive?
And some more details which are hard to discover in your own text.
What are the differences between copyediting and proofreading?