Vector graphics
Vector graphics are made up of paths. Each path is basically a line with a start and end point, curves, angles, and points that are calculated with a mathematical equation. These paths are not limited to being straight—they can be of any shape, size, and even encompass any number of curves. When you combine them, they create drawings, diagrams, and can even help create certain fonts.
These characteristics make vector graphics very different than JPEGs, GIFs, or BMP images—all of which are considered rasterized or bitmap images made up of tiny squares which are called pixels or bits. If you magnify these images, you will see they are made up of a grid (bitmaps) and if you keep magnifying them, they will become blurry and grainy as each pixel with bitmap square's zoom level grows larger.
Computer monitors also use pixels in a grid. However, they use millions of them so that when you look at a display, your eyes see a picture. In high-resolution monitors, the pixels are smaller and closer together to give a crisper image.
How does this all relate to vector-based graphics? Vector-based graphics aren't made up of squares. Since they are based on paths, you can make them larger (by scaling) and the image quality stays the same, lines and edges stay clean, and the same images can be used on items as small as letterheads or business cards or blown up to be billboards or used in high definition animation sequences. This flexibility, often accompanied by smaller file sizes, makes vector graphics ideal—especially in the world of the Internet, varying computer displays, and hosting services for web spaces, which leads us nicely to Inkscape, a tool that can be invaluable for use in web design.