ok so lets say you want to take a picture of something, say a pumpkin.
look at the picture in your camera and divde your screen up like a tic-tac-toe game. there should be 3 colums down and 3 across (hence the rule of 3rds)
when you take a picture, put the subject in one of the 4 places where the columns cross. Why? I learned in a photo class in high school that those 4 spots are most pleasing to the eye, and those are the spots that the eye goes to first when looking at a picture. Therefore you want your main subject on one of those spots.
Thats basically the rule of thirds! Just be careful,there are other elements that play into the picture such as light, contrast, etc. I find that the rule of thirds works best when you have a non moving object or when you take pictures of people sitting still.