It's one of the quintessential questions in the minds of many first-time art students, really. It's also one of the most oft-voiced critiscizms of a student's work (right after "you need to spend more time on figure-drawing").
When an instructor or an art director tells you a piece needs more "polish" what they are saying is that it looks unfinished to the outside viewer. As anyone with an artistic bent knows, in the eye of the creator, a piece is never really done, as the artist you can always find ways to improve it.
But when someone on the outside feels that it's not quite done, well, then maybe they have a point.
Many times it's simply a question of adding the hands and feet (you KNOW you've left the hands and feet off a character sketch at least once), sometimes it's the linework that needs a boost, or the addition of tone and texture.
In some cases it may just mean that the piece needs *more*. More detail, more consideration. You may need to "push" the piece further (yet another indefineable criticizim that is no less valid for it's fuzziness) which usually means you have to keep noodling with it.
As an instructor, it is entirely possible to spend an entire afternoon picking apart a student's work. Pointing out where a line could be thicker, the tone could be more even, the perspective is off, the eyes not aligned right, the fill-light needing more emphasis...
But what you get then is a student trying to duplicate exactly what the instructor does. It's helpful, especially at the very introductory levels, but once you pass the basics it can start to stifle a students' own style.
It can stall the lerning process and send the student into rounds of nitpickery, as opposed to accepting the mistakes as serendipity and moving forward (sometimes it's the mistakes that make a piece brilliant in the end).