Sorry, it’s not the prelude to a “graphic” joke… This is a common question about image types that comes up and one that lacks a lot of good explanation out there. This article does a good job of explaining it with some nice visuals: http://designwashere.com/design-battle-vector-vs-raster/
But, if you want the quicker punchline, here is the brief breakdown of each:
Raster: This term describes any image that is composed of static, colored “pixels” (small dots), such as jpg, png, bmp, or tiff files. These are typically altered in Photoshop, are usually photographic images, but are also used in websites for logos and graphic elements. Being that raster images are composed of static “dots”, they typically do not work well when the image needs to be blown up, as it blows up the size of those dots (causing “pixelation” or blurring). Raster images are when dpi/resolution is crucial. Typically printing resolution is 300 dpi, while web uses 72 dpi (this is why images grabbed from websites do not typically work for high-resolution printing purposes).
Vector: This term describes graphics that are composed of mathematical calculations that become smooth lines and shapes (instead of pixels, as in Raster images). Since they are created this way, they can be scaled indefinitely and color-separated without losing resolution which is fantastic for logos, etc. They can be eps or ai format files. Vector images are typically altered in Adobe Illustrator (hence the “ai” file). They are often simpler graphics like logos, but can also be quite complex artwork (see the article above for examples). Vector images are imperative for printing processes such as screenprinting that use spot colors, or for large-scale signage.
I hope this helps! – Jen