Vector graphics consist of lines and curves that are described to programs according to their geometric characteristics. When you edit vector graphics you edit these geometric characteristics. You can move, resize, or change the lines and curves without losing quality.
Vector graphic are resolution-independent - that is to say, they are not defined by a fixed number of pixels and so are automatically scaled to appear crisp and sharp on any output device and at any resolution. As a result, vector graphics are the best choice for type (especially small type) and bold graphics, such as logos, which require crisp, clear lines that can be scaled to many sizes.
Programs that create vector files are draw programs like Corel Draw, Adobe Illustrator etc.
N.B. Because computer displays are made up of a grid of pixels, both vector and pixel images are displayed as pixels on-screen. Vector-based programs render their shapes into pixels for display.