Assume that you aim your putter perfectly at your target at address.  Your putting stroke will have a stroke path and some degree of face rotation relative to that path.  Your desire, then, is to create a stroke path and face rotation that will allow the putter face to be aimed at your target at impact - consistently.

Every putter has some lie angle to it - the maximum lie angle a putter can have is 80 degrees.  As a result, every "natural" putting stroke has some amount of arc to it.  How much Face Rotation you have related to the arc of your stroke is important to consistently hit putts at your target.  Your putter face can either be square, open, or closed relative to your putting path.

The Science and Motion Sports (SAM) PuttLab site recently released the 5th in their "Fundamentals of Putting" training series, here is the link to this information:

  SAM PuttLab "Fundamentals of Putting" - Putter Face Rotation

The key concept in this article is that of "natural absolute face rotation."  If you are able to create a natural arc stroke, and do not manipulate the putter face with your arms and hands, then you can naturally keep the putter face square to the arc throughout the stroke.

There are two major elements of putter fitting that can affect the amount of face rotation in a putting stroke.  One is Putter Length.  If you use a putter that is too long for you, you are likely to be creating more face rotation than you need.  The second is Putter Design.  Henry Statina, an Edel putter fitter, recently wrote a series of articles on putter fitting - one of them on matching your putter to your path:

  Henry Stetina - Pick a Putter That Matches Your Path

Henry notes that putters with a lot of Toe Hang tend to be better for golfers with more arcing strokes, and Face Balanced putters tend to be better for golfers with a small amount of arc in their strokes.

One final thing - a Straight Back, Straight Through Stroke?  Well at one time this was the rage.  But now most knowledgeable putting experts agree that if you are creating this type of stroke you are manipulating the putter face - and so will likely create a less consistent stroke.