"Right tributary" and "left tributary" (or "right-bank tributary" and "left-bank tributary") are terms stating the orientation of the tributary relative to the flow of the main stem river. These terms are defined from the perspective of looking downstream (in the direction the water current of the main stem is going).
In the United States, where tributaries sometimes have the same name as the river into which they feed, they are called forks. These are typically designated by compass direction. For example, the American River receives flow from its North, Middle, and South forks. The Chicago River's North Branch has the East, West, and Middle Fork; the South Branch has its South Fork, and used to have a West Fork as well (now filled in).
Forks are sometimes designated as right or left. Here, the "handedness" is from the point of view of an observer facing upstream. For instance, Steer Creek has a left tributary which is called Right Fork Steer Creek.