Vector graphics is the use of polygons to represent images in computer graphics. Vector graphics are based on vectors, which lead through locations called control points or nodes. Each of these points has a definite position on the x and y axes of the work plane and determines the direction of the path; further, each path may be assigned a stroke colour, shape, curve, thickness, and fill.

What is a vector image?
Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygons—all of which are based on mathematical expressions—to represent images in computer graphics. Vector graphics are based on vectors (also called paths), which lead through locations called control points or nodes.

What is a vector file format?
Vector files such as AI and EPS can remain editable so you can open them back up in Illustrator and edit any text or other elements within the graphic. With images that contain text that are saved as a JPG, PNG or GIF, you would not be able to reopen and edit the text.

What is a vector graphics software?
A vector graphics editor is a computer program that allows users to compose and edit vector graphics images interactively on a computer and save them in one of many popular vector graphics formats, such as EPS, PDF, WMF, SVG, or VML.

What is a vector and what are they made from?
The difference between vector and raster graphics is that raster graphics are composed of pixels, while vector graphics are composed of paths. A raster graphic, such as a gif or jpeg, is an array of pixels of various colours, which together form an image.

Also see: What are vector and raster maps?