What Is Vector Data?

Vectors are line segments minimally defined as a starting point, a direction, and a length. They can, however, be much more complex and can include various sorts of lines, curves, and splines. Straight and curved lines can be used to define geometrical shapes, such as circles, rectangles, and polygons, which then can be used to create more complex shapes, such as spheres, cubes, and polyhedrons.

Vector Files Came First
Vector file formats have been around since computers were first used to display lines on an output device. CRTs, for example, were first used as computer-driven output devices in the 1950s. The first CRT displays were random scan devices similar to oscilloscopes, capable of producing images of mathematical and geometrical shapes. Vector display devices provided output sufficient for the needs of computer users for many years after their introduction, due to the limited range of tasks computers were called upon to perform.
At some point the need to store vector data arose, and portable storage media such as punch cards or paper tape were pressed into use. Prior to rendering time, an image was logically subdivided into its simplest elements. At rendering time, the image was produced and maintained by drawing each of its elements repeatedly in a specified order. At storage time, data was readily exported as a list of drawing operations, and mathematical descriptions of the image elements--their size, shape, and position on the display screen--were written to the storage device in the order in which they were displayed.