I am trying to figure out what a roll-back is associated with the clean-up badge? I've surfed the questions and answers with no avail.
This is one badge you probably shouldn't go about trying to create, but given the right scenario it's easy enough to get. You need a post (owned by anybody) that was edited (by anybody) but the edit was a bad deal and the best thing for it is to roll back to a previous revision from the edit history page.
This is most useful in the event of A) deliberate vandalism that made it past the review process or B) edits that clearly misunderstood the post they were 'improving'.
I earned mine when somebody else edited my question, and I rolled it back to my previous version. The history can be seen here
First, a relevant question on MSE.
To give you a sense of the rarity of rollbacks, the percentage of my edits that are rollbacks at the time of this writing is about 0.8%. The other three people who have interacted with this question sit at 1.1% (Curiousdannii), 4% (Caleb), and 0.2% (David).
Now, to give you a sense of the types of circumstances that can result in such an action, I'll offer my own rollbacks as an example:
I got my badge on a question asked by a new user who, after receiving satisfactory answers, edited their question into an entirely new one.
I rolled back another edit that added the now-gone "dogma" tag (which was as useless and therefore removed (manually, question by question) by the community) as well as another tag that I generally find useless.
The next one I rolled back was on my own question. The problem wasn't that the edit was harmful, but that it was superfluous and I preferred my original formulation. If it wasn't my own question, I would have let it stand and allowed the OP to make the judgment call.
The last one I rolled back was because it was an old question, on-topic when it was asked but then later off-topic as the site's scope changed, and edits to make it on-topic again had invalidated all of the answers. Yeah, a little complicated. I wasn't happy with the edits and asked for people to give more votes (whether up or down) to a pertinent Meta post. After the Meta post got to a score of about 8, I initiated the rollback and voted to close.