Vector Graphics are image files created using geometric elements such as points, lines, Bézier curves and shapes - rather than a mapping of how the image would appear (such as a bitmap or raster image).
Since Vector Graphics are not based on pixels, they do not change resolution when they are scaled up or down. Vector Graphics are also always consistent in file size, whereas bitmaps and raster images change file size depending on scale.
These qualities make Vector Graphics a preferred medium for computer generated graphics - but they must be converted to bitmaps or raster images in order to render them on a display, or print them on a printer.
Essentially: a bitmap of a line magnified gives a "lego" effect. Bottom image, a vector 1px line magnified equally: