Triglyphs and Metopes
Most Greek temples have a pattern under the pediment known as triglyphs and metopes. The triglyphs alternate with the metopes across the front of the temple. Triglyphs (TRY-gliffs) have three parts, and then in between the triglyphs are the metopes (MET-oh-peas).
Why have triglyphs and metopes at all? They started as a natural part of wooden temples, back in the Dark Ages when people in Greece were building temples out of logs. The triglyphs were the ends of the wooden beams of the roof, and the metopes were the spaces between the beams. When architects began building stone temples, they wanted them to look familiar, so they kept the pattern, even though it had nothing to do with the structure anymore.
Sometimes (as on the temple from Agrigento) the metopes are plain. On other temples, like the one here (also from Sicily), the metopes carry carved mythological scenes. The center metope here shows Perseus killing Medusa.
Metope from the Parthenon
On the Parthenon, the carved metopes represent a battle between the Lapiths and the centaurs. The Parthenon's all about the battle between civilization and barbarism, order and chaos, and here the Lapiths (because they're men) represent order and the centaurs (because they're not men) represent chaos. On some of the metopes the Lapiths are winning, and on others the centaurs are winning.
Another metope from the Parthenon
To people in ancient Greece, architecture was an important part of order. Rhythm and mathematics were part of that order, and so they were important parts of civilization. People thought of temples as a kind of visual metaphor for music. In this metaphor, triglyphs and metopes provide a rhythm that steadies the melody of the pediment carvings.
Learn by doing: Choose a Greek myth to illustrate in metopes with triglyphs between them
More about the Doric order
Ancient Greek Architects at Work, by J. J. Coulton (1982). An interesting look at how Greek architects worked.
Greek Architecture, by A. W. Lawrence, R. A. Tomlinson (5th edition 1996). Might be a bit out of date.