The rule of thirds is a great way of taking fantastic photographs! The idea goes back to the late 1700′s so it’s not a new idea but one that has worked well over the years for paintings and in more recent times, photography.
The idea is that you split the photograph you’re about to take in to thirds, both horizontally and vertically (some digital cameras have these lines as a setting) and it should look something like this:

The dots indicate the best place to put the subject of your photo, so if you’re taking a photo of a person, instead of putting them in the centre of a photo you should put them where one of the fours dots is.
Give it a go and you’ll soon see that you’ll get some better more interesting photos.
One thing to remember is that rules are meant to be broken! If you want to put the subject of your photograph in the centre then do so! The human eye also likes things that are symmetrical so there’s nothing wrong with putting the subject in centre and completely ignoring the rule of thirds!
The whole idea of this rule is to simply give you another option of taking a great photo, but at the end of the day you should take photos how you like.