Your copy editor reads your work thoroughly, line by line, checking for more than just spelling and grammar mistakes. She ensures that your characters remain consistent throughout the story, that the setting and plot details are plausible, and that your voice and style are consistent to the end.
Examples of how a copy editor can help your manuscript:
She helps ensure that your character doesn't have brown eyes on
page three and green eyes on page 153.
She helps keep the details of your fantasy world consistent, such
as the types of magic used and the methods for invoking spells.
She keeps an eye out for anachronisms in historical fiction, such as
technology or slang that did not exist in the period portrayed.
She points out that a horse can't gallop for twelve hours straight,
so your characters have to take breaks while travelling.
She keeps your narrative from slipping into third person when it
began in first, and points out instances of "head-hopping".