Visualization of Curl
This is a great visualization and explanation, of the curl of a vector field:
If you interpret a vector field as the flow of a fluid, then you can interpret the curl as a measure of the tendency to rotate at a given point.
One way to think of this is to imagine a tiny sphere, or paddle-wheel, fixed at a point in space, and then consider how that object would rotate if subjected to the flow of fluid as given by the vector field.
This write-up and series of animations from MathInsight.org are very useful in attaching some intuition to this complex idea.