There are two types of balance: symmetrical and asymmetrical.
With formal balance, a picture has all of the same elements on both sides.
For example, imagine you were looking at a portrait of someone facing straight ahead. If you were to fold that picture in half, you would see the same image on each side. Meaning, both sides of the folded photograph would show half of a shirt, half of a mouth, one ear, and one eye, etc.
Asymmetrical balance is the balancing of unsimilar or contrasting elements in a photograph. If you folded the picture in half, you would most likely see two totally different objects.
The two photographs above have a symmetrical balance, because you could fold the picture, and see the same thing on both sides. Whereas the photos towards the bottom of this page have more of an asymmetrical balance.
With asymmetry, one side of a photo is more heavily weighted than the other.
The line of symmetry lies more to one side, than in the center.
Even if a picture isn't perfectly balanced, sometimes that makes it more interesting.