This feature is an extension of more basic Page Permissions.
An Access Control List features gives you fine-grained permissioning control. You can set up lists of users (perhaps in groups or roles) who are allowed to access to certain parts of your wiki, for operations such as viewing, editing, creating new pages, etc.
For many purposes such fine-grained control is probably not necessary. Note that one of the great things about wiki software is its “Soft Security” approach. If you are tempted to go locking down and restricting editing of your wiki, perhaps you need to think again. Would it really do any harm to allow everyone to edit this page? Websites like Wikipedia have demonstrated that with a “watch page” feature and enough people watching each page for questionable changes, bad edits can be reverted quickly enough so that locking down pages is not required.
On the other hand, ACL are a powerful tool to avoid scripted attacks from spambots or vandalism from anonymous users. This is especially true for user communities smaller than Wikipedia's in which a posteriori moderation is less effective. ACL are also an essential feature for wiki engines used in contexts other than collaborative projects, e.g. as a backend for personal or admined websites, internal knowledge bases and any other kind of partially or fully moderated use.