Vector art is drawing, painting or illustration created using a Vector application such as Adobe Illustrator. It is not a form of Art or an Art movement like pop art or modern art. It merely involves creating art by using a computer and specific type of applications called Vector Applications to create art. It's a scalable, and editable image that provides graphic designers freedom when it comes to graphic design and illustration. Vector images are ideal for graphics such company logos and artwork that often requires scaling.
A vector image is broken down into a lot of geometric shapes which are created by these mathematical equations, rather than pixels, rendering the highest quality possible. Vector images are not resolution dependent. So, each vector object is fully scalable and will give a graphic designer the ability to resize artwork without the loss of image quality.
It is common practice for graphic designers to use vector based images as the starting point for any new graphic design project, such as logos. However, since you cannot scan a drawing or image and save it as is, a vector graphic designer must create them from scratch by using high-end drawing software such Adobe Illustrator. Vector art files or logos are usually saved as: .EPS, .AI, .CDR, or .SWF, file extensions.
So, why would you want to work with a designer who does not create logos or other images in vector format? The answer is you don’t. If the designer is limited to what he can do with the design of your image, then so are you.