Raster vs Vector

Raster and Vector are both different type of graphics that are found in different applications for graphic design. 

Raster graphics are found in Photoshop, where these images and pixels are not done with mathematical calculations, and so will get pixilated if enlarged or changed in a way.
Vector graphics on the other hand are done using mathematical calculations and can be enlarged, reduced and still keep its proper shape and detail.

When drawing with pixels, like said before, you are at risk of losing clarity when enlarging your image.

When drawing with vectors, this will not happen as it uses a system of mathematical applications. So if you were designing a poster, business cards and a logo for a particular company, you would have to use Vectors because you will need to enlarge and shrink the logo size for posters and business cards as to keep clarity.

Since raster images' dimensions are measured in pixels, suppliers may have specific size requirements for their processes. They might require a specific pixel resolution: a specific amount of pixels within each inch.  The amount of pixels within each inch in the image represents the image resolution or PPI(pixels per inch)  

File sizes are also different from each other. In raster images like photoshop, the size is about 200MB for example, and in Vector images like illustrator, the size is below 100MB.

Raster graphics is used for photo manipulation like the example below. This is useful as because of pixels, you will not able to tell the full detail even with a magnifying glass. This helps perfect the illusion trying to be portrayed.

In order to determine what size your raster image must be for good quality printing, you have to multiply the resolution required by the area to be printed. For example, magazine size is 300PPI and you have a space of 5inches on the magazine, u multiply them and get 1500(pixels wide).