Updated March 1992 by SIC;
Original by John Blanton.
Stars, except for the Sun, although they may be millions of miles in diameter, are very far away. They appear as point sources even when viewed by telescopes. The planets in our solar system, much smaller than stars, are closer and can be resolved as disks with a little bit of magnification (field binoculars, for example).
Since the Earth's atmosphere is turbulent, all images viewed up through it tend to "swim." The result of this is that sometimes a single point in object space gets mapped to two or more points in image space, and also sometimes a single point in object space does not get mapped into any point in image space. When a star's single point in object space fails to map to at least one point in image space, the star seems to disappear temporarily. This does not mean the star's light is lost for that moment. It just means that it didn't get to your eye, it went somewhere else.
Since planets represent several points in object space, it is highly likely that one or more points in the planet's object space get mapped to a points in image space, and the planet's image never winks out. Each individual ray is twinkling away as badly as any star, but when all of those individual rays are viewed together, the next effect is averaged out to something considerably steadier.
The result is that stars tend to twinkle, and planets do not. Other extended objects in space, even very far ones like nebulae, do not twinkle if they are sufficiently large that they have non-zero apparent diameter when viewed from the Earth.