In short, a vector is a scalable element that doesn't lose quality when stretched to any size. Primarily used for simple logos and icons, they have a small file size, making them quick to load on websites and apps.
In contrast, a photograph is a raster image, which uses individual pixels to display colour. As these square pixels are stretched, the blocks become bigger, producing fuzzy edges and a reduced quality.
It is not possible to make a vector out of a raster photo (jpg, png, or gif image), as the pixels are already defined; converting these to a vector file format (sgv, ai or pdf) will not fix this. You can save vectors as a raster, as this flattens the image into pixels.