Copy editing is about making your manuscript follow the rules of grammar and punctuation. Editors will also trim unnecessary words and change passive sentences to active ones.
For fiction, a copy edit may include catching continuity errors as well—for example, your hero has blue eyes on page 10 but green eyes by page 100. For non-fiction, your copy edit might check and flag potential factual errors.
If you have big issues still in your book at this point, your copy editor is going to leave them there. It’s not their job to fix them. A good copy editor will brave your wrath to suggest you should have a developmental edit or a line edit done first. Some of them, if they have the skills, will fudge a little and give you a line edit even though you only paid for a copy edit if they see you need it and they have enough time in their schedule. Don’t count on this. They may not have the time, and you’ll only get what you paid for. (Plus, is it really fair to expect them to do more than you paid for?)
At this time, I no longer personally do copy edits, but my husband does. He writes a weekly grammar column for my blog if you’d like to learn more about him and what he can do for you. You can also contact him through his website at https://saylorediting.wordpress.com, or you can email him to talk about rates and availability at christopher.saylor21 [at] gmail.com.