Remember polygons from grade school math? Here's a little refresher for those of us who spent too much time sniffing those magic markers during class. A polygon is defined as a closed figure made by joining line segments, where each line segment intersects exactly two others. The points where the line segments intersect are known as vertices.
The most basic polygon is the triangle, and the nice thing about triangles is that once you have one, adding others is a breeze. Given a single triangle, you can create another vertex outside one of the triangle's edges and use the edge's vertices to connect to the extra vertex, defining the rest of a second triangle. The result is two triangles that only need 4 vertices and 5 line segments because they share one edge.
These 2D polygons are the building blocks for 3D objects. It takes hundreds or thousands of polygons to create a single 3D object. The more polygons used, the more detailed the image, but 3D objects with high polygon counts eat up more memory and processing cycles.
Exactly 998 polygons (in the full image)!
Programmers have to keep an eye on polygon counts to keep gameplay smooth. It wouldn't be very fun if a game slowed to a crawl every time a high polygon boss came appeared on the screen. As hardware improves, programmers will be able to use more and more polygons to create more detailed games.