The above graphic* is a good visual of the main difference between vector & raster. Raster images are what you naturally get with photos with file extensions such as JPG, PNG, TIFF. Vector file extensions include EPS, PDF**, and AI.
Vector – created with mathematic equations by an app, independent from resolution. In other words, enlarging these vector images will not cause it to pixelate.
Raster – created with pixels by an app, resolution-dependent. In other words, the higher the dots or pixels per inch a raster image has, the better the quality it is (lesser pixelation). Enlarging raster images will increase pixelation, making it lower quality.
Generally, graphic designers cannot convert raster images to vector images. Raster Graphics will have to be created from scratch in a vector-editing app to make them a vector. Photos currently cannot be converted from their natural raster form to vector.
*Graphics are another name for digital drawings or illustrations.
**You may already know that PDF files can hold both vector and raster images. Technically all vector file formats can hold both image file types but raster can only hold raster.