Definitions

Vector:

Images that are built with paths, points and vertices, and that use algorithms to define shapes, colors and sizes. Vectors generally are scalable without loss of quality. Common uses for vector are logos, clip-art or other simplified illustrations. Also, text in a document is usually in vector format.

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Raster:

Images that are built on a grid of pixels, single points defined color and position. Scaling a raster image, smaller or larger, affects the quality of the output. This is because the pixel grid has to be redefined and the entire image is remapped. Photos or "web" graphics are usually raster images.

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Resolution:

Raster images are further defined by their resolution, or dpi (dots per inch). Web images generally have a low, 72 dpi resolution. Images for print should be built at a 200-300dpi, a med-high resolution. One way to think of resolution is that it determines the size at which an image can be printed without loss of clarity. Generally speaking, the higher the resolution, the better the quality when printed.*
In the example below, notice how the pixels become more visible when the image size is increased.**