Sinuosity is a measure of how much a river (or other linear feature) deviates from being straight. A truly straight river or road has a sinuosity of 1; as the number of meanders increases, sinuosity approaches 0.

I wrote a document describing how to determine the sinuosity of linear features years ago. I will update it for ArcGIS 10 as time permits, but the original document, written for ArcView 3.x and ArcGIS 8x/9x is available here.