Curve onto a surface of revolution which intersects all meridians under the same angle, e.g. a screw line on a circuit cylinder. You call it also Line of Equal Course.
The loxodrome onto the Earth sphere resp. onto the Earth ellipsoid is of great significance for navigation because a sea- or aircraft gets exercise on the loxodrome if its course over ground keeps constant what is mostly easy to manage with the aid of a compass. Such a loxodrome converges to the poles in spiral windings (figure from [3] under literature).
Pedro Nunes, who conceived this curve in 1550, had still the misconception that the loxodrome is the shortest connection between two points on the Earth sphere (orthodrome).
The loxodrome appears as a straight line onto sea charts (Mercator maps) and so enables particularly simple graphical solutions to nautical tasks.