Sometimes, instead of getting an offer or a rejection from an agent or editor, a writer will get a revision request. This usually means that the agent/editor is intrigued by the project and finds potential in it, but sees a substantial amount of work before the project is saleable.
In the absence of an offer, the author doesn't have to revise; she is free to take her project elsewhere. But she may decide to try the revision, especially if the editorial suggestions ring true.
A couple of things to remember in these situations:
--If the story just needed a few minor tweaks, the agent/editor probably would have offered. Therefore, it's likely that considerable changes are expected.
--The revision is likely to need work on more than just the specific examples mentioned in the request letter. The agent/editor is probably looking for a true "re-envisioning," a multi-layered improvement.
Suppose the letter says, "I think Michael needs to be a stronger character throughout the book. For example on page 47, he gives way to Trudy, and on page 121, he again lets others drive the plot." It may be tempting to make a change on page 47 and another on page 121, and call it a day. But "throughout the book" means just that, and pages 47 and 121 are just examples, meant to illustrate the problem. The agent/editor doesn't expect to provide an exhaustive list of everywhere in the story that Michael needs to take charge; he/she expects the writer to do that.
In some ways, a revision request is a test: can the writer handle the kind of editorial work required to get a book into publishable shape? Does he take the initiative on making the story better everywhere he can? Even when a publisher acquires a project, there is a fair amount of editing still ahead for the writer. A writer who is ready to tackle that work is more likely to be ready for publication.