Chances are, if you've ever worked with a designer, at some point they've asked you for a "vector version" of your logo. The conversation generally goes something like this:
Client: Hey Designer  Attached you'll find a copy of our company logo. Looking forward to seeing those proofs!
Designer: Thanks Client, but the image you provided is a low resolution copy of your logo. This image will not reproduce well on the brochure you'd like printed. Can you please forward me a vector version of your artwork?
Client: Sure... Let me see what I can find.
Days later...
Client: What's a vector?
This post is designed to answer that question.
There are two kinds graphics:
 Raster  A collection of dots or pixels
 Vector  A collection of paths
Raster graphics use a grid of individually colored pixels to represent an image, whereas vector graphics use a mathematical equation between paths to represent an image. Vector graphics, because of their mathematical composition, can scale up without distortion. In contrast, the larger you scale a raster graphic, the more pixelated the image appears. This concept is illustrated in the example below.
When we magnify the sushi graphic above to 1000% it's easier to see the distortion/pixelation that occurs in a raster image.
Raster Images 
Vector Images 

Composition  Collection of individually colored dots or pixels  Collection of paths that form a shape 
Resolution 
Concentration of visual information within a given area 
Defined by a mathematical equation, not by dots or pixels Completely scalable 
Common Uses 
Photographs and images with highlights and shading 
Graphics of uniform color, layouts, type/text, and illustrations 
File Size  Larger  Keeps track of individual pixel info  Smaller  Keeps track of mathematical equation 
File Types 
.BMP  Windows Bitmap 
.EPS  Encapsulated PostScript .WMF  Windows Metafile .AI  Adobe Illustrator .CDR  CorelDraw .DXF  AutoCAD .SVG  Scalable Vector Graphics 