The complete question is in the title this time (well, I do know what "Approve" means :-), I am interested in how community can review something)
When users with 2k rep review suggested edits, they have the option to "improve" them. On the improve page there is a check box marked "This edit was helpful", if the reviewer leaves that box checked the Community user approves it.
Take for example this edit. Eliah edited (or improved) your edit, so his decision is marked "Edit", but since he kept the "Helpful Edit" check box checked, Community approved your edit.
Community can also reject edits. This usually happens when you suggest an edit at the same time someone else edits that post. If the second editor has less than 2k rep Community will reject his edit, but if the second editor is the OP or a user with more than 2k rep your edit will be rejected by Community.
This means the edit was improved by another user, who marked it helpful.
When that happens, the edit suggestion (and editing history for the post) shows the Community♦ bot as approving the edit. In the editing history, the reviewers improvements are shown as an immediately subsequent edit.
Similarly, when an edit is improved by another user who marks it unhelpful Community♦ rejects it and the improved version is applied as the reviewer's own edit, with the suggestion not appearing in the post's edit history.
See my answer here for more details on what options reviewers have when reviewing suggested edits. To excerpt the most relevant part:
- They can decide they don't know if it's good, and do nothing, leaving it for another reviewer to consider. This is not recorded in any way in the post's edit history, as nothing was done. The reviewer simply looked at the edit and decided not to review it.
- They can decide your edit is good and approve it.
- They can decide your edit is bad and reject it.
- They can decide your edit is helpful but should be improved. They then apply their further edits to yours. The editing history shows this as the Community user approving your edit and the reviewer editing the post themselves immediately afterwards.
- They can decide your edit is not helpful, but still use it as a basis for their own edit. The editing history shows this as the Community user rejecting your edit and the reviewer editing the post themselves immediately afterwards.