Vector graphics are stored in the computer as a set of mathematical formulas describing the shapes that make up each image. When you display a vector graphic on the screen or print it, these formulas are converted into the patterns of dots you can see. Because the dots are not specified unit! you display or print the graphic, you can change the size of the image without any loss of quality, and the image will always appear at the highest resolution of whatever screen or printer you're using. The term vector graphics means exactly the same thing as object-oriented (or just object) graphics.
The contrasting term is raster graphic (the terms raster and bitmapped are synonymous). In a raster graphic, the actual dots that make up the image you see are defined when the graphic is created, so the resolution is fixed; changing the size will make the image look coarse or muddy. See paint program for an example illustrating the fixed resolution.
Most Macintosh people use the terms object-oriented and bitmapped rather than vector and raster. Most PC people use both pairs of terms interchangeably.