The question is pretty straightforward: What makes a locus in the complex plane a contour?
I read through the Wolfram MathWorld pages for both a contour and the Cauchy integral formula (the page about residue theorem was too lofty for me) but neither of these define any criteria.
I completely understand that the contour is the curve in the complex plane that is the domain of integration for a line integral of a complex-valued function. I am also under the impression that a locus must be closed to be a contour, but I am not sure.