Vector graphics is the term given to Graphics or artwork that have be generated using mathematical or geometric shapes programs like Adobe illustrator. They are very good at producing such graphics. The advantages of creating vectored graphics is that the file sizes as usually a lot smaller and the print quality is so much higher then pixel generated artwork graphics. Other advantages are scaling of artwork, you can scale the artwork can size as vectored graphics are mathematical there for you will retain the quality of the print. Other items like fonts work in the same way.

File  types associated with Vectored graphics are .AI .EPS .PDF