A small circle of a sphere is the circle constructed by a plane crossing the sphere not in its center. Small circles always have smaller diameters than the sphere itself (compare great circle). Small circles cannot be parallel, because parallelism doesn’t exist in spherical geometry. They may look parallel but they are no more parallel than concentric circles on a plane.
The small circle does not have the smallest curvature and hence, a segment on its circumference does not represent the shortest path between two points on a spherical surface.
Except for 90 Degrees North or South and the Equator, all parallels of latitude upon the Earth are small circles (or at least close approximations, as the Earth varies from a true sphere to a relatively minor extent). An observer standing on such a circle and viewing its path toward an unobstructed horizon, would perceive it to bend away from his line of sight, an effect of the inequality between the amount of curvature to his left and right.
By contrast, all meridians of longitude are great circles.