When signing the first contract, authors will always ask what's next, what's the next step in the publishing process, and usually it's edits. While certainly every publisher and every editor is different, here's what you can typically expect.
Revisions: These usually come from your acquisitions editor, the editor who made the offer and "bought" your book. Revisions can be as intense or as simple as the editor feels is needed, and how revisions come can differ from editor to editor. Some might print out a copy of the manuscript and make marks all over the page, while others could send a simple two-paragraph email explaining what needs to be done. Personally, I always fear the shorter revisions, they usually contain the most work. Things like "The entire second half of the book isn't working," instead of specifics like "Tone down the character in this scene."
Line Edits: Once revisions are turned in, and the editor finds them acceptable, she'll do line edits. This is where she scrolls through the manuscript to make sure there are no other problems or inconsistencies. She'll look for things like a change in dress color and make sure that a plot change is carried through. Sometimes line edits will be sent back to the author, but more often they'll simply be made and sent to the copyeditor so that you can look at line edits and copyedits at one time.
Copyedits: These are done by a freelance copyeditor. This is when the nitty-gritty of the book is taken care of. The copyeditor's job is to check grammar, punctuation, spelling, and consistency. If you have a lot of odd spellings or characters in your book, I would always recommend a style sheet be submitted with your manuscript to the copyeditor so that she knows the spelling of names, or the spelling you choose, and can keep things consistent from book to book.
Proofreading: This is when the book has been taken to the printer and designed into final pages. You have one final chance to review the book, to proofread, and make sure no errors were made in the printing, layout, and design. At this point you cannot make major plot changes, but simply correct small, minor errors.