A type of wiki contributor, a wiki curator acts in many of the same ways a museum curator does. Maintaining the artifacts (the articles), researching them, arranging them into interesting dioramas (the indexes), and so on.
There are generalist curators and specialist curators. Specialists have a deep interest in a specific medium or a specific genre and don't do much curating outside that interest. The interests of generalist curators are wider. Or perhaps they just wander.
If a wiki isn't attracting curators of either type, it just isn't working.
How a curator works on a wiki is by tracking certain pages on their watchlist and looking out for things like bad examples and clumsy edits. The ultimate goal of the curator is to protect a page from eventual edit wars or deletion due to quality or other concerns.