Vector files include curves, points and shapes in a relative to each other position. This means that every time when you enlarge or shrink the image you will end up with a nice-looking, unwrinkled lined image. In other words vectors are not formed by pixels, the quality stays the same always no matter how small the object is.
This is useful for a brand design because you would not want your customer to be able to count the pixels on that advertisement you made.
Vector images are the best option for logo designs and printworks. You should operate with them to create great brochures, posters and billboards. However, you have to use drawing software such as Adobe Illustrator and Inkscape to create a vector image or to transfer usual raster(pixel based) into vector photo.