Simple contour
A contour that does not cross itself, except that a closed contour's two endpoints may coincide.
A contour is simple if it does not cross or touch itself anywhere along its length -- distinct parameter values t_1\ne t_2 always give distinct points z(t_1)\ne z(t_2) -- with one exception allowed: the first and last points may coincide, which is what makes a simple contour closed rather than open. Simplicity is what stands between a curve and a genuine "boundary of a region", since a self-intersection would make inside and outside ambiguous.
Examples
The unit circle is a simple, closed contour: it never crosses itself, and its start and end points coincide.
A figure-eight curve is not simple, since it passes through its center point twice.
See also