In order to put a page in context, searching for BackLinks is often useful.
When you want to rename a page, you have to change the links to that page, too. Most wikis use a very simple storage model where the pages are stored as plain text, thus changing all the links usually means you need a global search and replace operation. Most wikis don’t offer these for ordinary users, because they can cause great havoc in short time (it may not be ReversibleChange).
In this situation, you want to search for all backlinks, so that you can change them manually.
Using plain search for a page is a useful simplification. It works because the page title will be part of every link and URL to the page. It fails if the page names are so common that a plain search will find many false hits.
Do people use backlinks to put a page into context? I never do. I only do this to verify the lin structure. – AlexSchroeder