There are two main types of symmetry, bilateral and radial. Pietro Perugino’s Christ Handing the Keys to St. Peter, 1481-82, will help to demonstrate the first of these.
This work is highly symmetrical or, put another way, has strong bilateral symmetry. This means that if we were to draw a line down the middle of the image, the two sides would roughly mirror one another. Notice in particular the way that the buildings in the background are painted to make the work symmetrical:
Some works, though, are radially symmetrical, that is, symmetrical around a center axis, like a daisy or a rose windows in a Gothic church: