Line is a mark made by a pointed tool - brush, pencil, stick, pen, etc. - and is often defined as a moving dot.
It has length and width, but its width is very thin compared to its length.
A line is created by the movement of a tool and pigment, and often suggests movement in a drawing or painting.
Line in Fine Art
Tobey's painting is all line. He actually drew with his brush, then repeated lines creating a complex pattern. Tobey's lines are the subject of the painting and are not used to outline shapes or objects.
Source: Elements and Principles of Design: Student Guide with Activities, published by Crystal Productions
Line in Graphic Design
Magleby and Company
This poster shows how just a few strokes of line can be used to effectively illustrate a swan. While the lines do not adhere to the anatomy of a swan, the image is unmistakable, and the simplicity and grace of the lines convey a feeling of tranquility.
There are no excess lines; the poster has just the number of lines needed to communicate this image. Particularly successful is the use of wavy lines to communicate a reflection on the water. Type is used sparingly (only along the left edge,) and only to provide needed information to the viewer.
Source: Design Basics for Creative Results by Bryan L. Peterson