The rule of thirds is not so much a rule but a guideline .This is one of the first things you should learn in photography, as it gives a basis for well balanced and interesting shots. It works both horizontally and vertically. But as always, rules are meant to be broken, the key is to know when and how. The main point is to not put your main subject smack in the middle of the frame.
Imagine a tic tac toe board, and place the main subject on one of it´s lines. When it comes to people the eyes are the most important.
One of the easiest things you can do with a photo that doesn´t use the rule of thirds, is to crop, you may find that suddenly the photo is soooo much better.
The rule of thirds also is great for negative space.
There may me times when you can break the rule of thirds, like in the photo below.