Vectoring means the images are scalable. A way to think of it is "One size fits all," you don't need to make images for every resolution there is. Take splash screens for example. Most games need to make a 640x480, 800x600, and 1024x768 screen. That's using bitmaps, where the image is an array of pixels and each pixel defines the color of that point on the screen. (If you took a 640x480 image and stretched it to 1024x768 resolution, there isn't enough image data to fill the empty spaces between pixels - so the picture becomes pixelated and grainy).
Using vectoring means instead of using an array of dots, it expresses the image in terms of lines, circles, and other shapes (known as vectors.) The sizes are relative to each other. The computer, when rendering the image, figures out how big in pixels each vector has to be, and renders at the correct size.
An example of where you use vector imagery is whenever you use the MS ClipArt. (That's why the image doesn't pixelate when you enlarge it). The computer figures out the absolute sizes of the elements in the picture and makes sure it appears fine.
A common vector/scalable image format are WMF files on Windows (most clip arts are WMF files). There are formats for other OS'ses too (can't remember the names of the formats though).
