I looked outside my window one night, and the moon was shining brightly, and it wasn't a full moon. But thats not the point. Really close to it was something that looked liked a star. It was really bright, and it gave off a white light, but the more I looked at it, the more I realized that it wasn't flickering or twinkling the way stars do. A few minutes later, I looked at it again, and this time it was smaller, less bright, and farther away from the moon. I know its not a satalite because I've seen those before and they move faster, and they give off the same amount of light all the time. If anyone has any idea what this thing could be, please tell me, because I really want to know.
Stars are, to all intents, infinitely far away and hence present themselves as points - thus the small changes in the atmosphere's refractive index caused by different patches of density and temperature of air make them appear to twinkle.
Planets, on the other hand, are relatively close by and (with the exception of the Moon and the Sun itself) whilst we cannot resolve any solar system body into a disk with the naked eye, they are still larger than (most) variations in the atmosphere, hence they don't appear to twinkle or the twinkling is much reduced.
The evidence suggests you saw a planet, quite likely Jupiter or Saturn.