Regular edits are immediate, and you only get a notification about those after they changed your post.

You can only approve (or decline) *suggested edits* by users who do not yet have the required [editing privileges](https://superuser.com/privileges/edit) to perform regular edits. These are placed in a queue for review by more experienced users, and only actually performed once approved.

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So, yes, there is an *approve* button, but only when the editing user does not yet have at least 2000 reputation.