Making amends is what we do when we've done something wrong, such as forget a partner's birthday, throw away our child's favourite broken object or sulk all through a dinner date. Making amends to a book is the same - you screwed up first time round, now you fix it. Amends is publisher-speak for amendments, which we usually think of as corrections. The connotations of 'making amends', though, gives the short form considerable emotional potency. Luckily, the phrase is usually 'doing amends'. You may see them called 'author corrections', too.
Amends are not the same as edits. They are generally a non-fiction phenomenon, for in non-fiction things can actually be wrong. In fiction, there are inconsistencies, implausible bits, lapses in continuity, but it's hard actually to be wrong as it's all a bunch of lies anyway. Non-fiction is not supposed to be a bunch of lies. Strangely, the term is extended to mean other editorial matters besies correcting errors of fact. Amends can included restructuring chapters, cutting material the editor doesn't like or adding material the editor would like if it were there. Making amends is your penance for being a less-than-perfect writer. Don't argue, just do it.