Vectors

A Vector is simply a connection in space.Vector graphics is the use of lines,points and curves which are all based to represent images in computer graphics. 

http://en.wikipedia.org/wiki/Vector_graphics

Above is an example showing effect of vector graphics versus raster graphics.Raster images are based on pixels and thus scale with loss of clarity, while vector-based images can be scaled indefinitely without degradation.

Basically if you change the size of a Vector image the quality stays the same.It is resolution independant.This is because they are composed of lines and curves.These vectors allow the vector file to be scaled without losing any quality of the image.

Vector graphics are best used for shapes and logos especially if scaling is involved.

Rather than being composed of pixels, Vector graphics consist of points, lines, and curves which, when combined, can form complex objects These objects can be filled with solid colors, gradients, and even patterns. Because the computer has a description of how the image should look, it can be redrawn at any size, in any position, without losing any quality. A vector graphic resized to 5 times its original dimensions is simply reproduced, exactly, at the new size.

Bitmap ‘RASTER’

 Bitmap images, also referred to as raster images, are pixel-based. This means that location and color information about the image is stored in individual pixels within a grid.You edit pixels rather than shapes or objects directly.

Raster images are resolution dependant in that they contain a specific number of pixels. Therefore if images are scaled ,they will lose detail and appear jagged. The pixels are tiny dots of individual colour.All these tiny dots of color come together to form the images you see. Below is an example of a bitmap enlargement.

   A Bitmap Image–shown zoomed in with the original size in the upper right corner. Notice the individual pixels that make up the image.

http://graphicssoft.about.com/od/aboutgraphics/a/bitmapvector.htm 

As you can see, when you enlarge the icon, as I have in this example, you can clearly see each individual square dot of color. Because bitmaps are resolution dependent, it’s difficult to increase or decrease their size without sacrificing a degree of image quality.

http://www.wikihow.com/Choose-the-Correct-Graphics-File-Format