The subject of this article originates from non-canonical sources. To find out about what is considered "canon" see LOTR:Canon.
The Shiltron is a tactical battle formation.
A shiltron was a defensive formation in which troops would form a circular or "shield-like" (hence the name) shape. The center of the formation was hollow to allow beset troops to fall back towards the middle if need be. It was used to protect the flanks of all the troops involved as it prevented the enemy from attacking any soldier's flank as his fellow warrior always guarded it.
Another clever circular formation that was used by all spearmen of middle earth was the porcupine formation; it combined the sheer impenetrability of a phalanx with the highly effective Shiltron. (Featured in Battle for Middle-earth game) It was mainly used as a last stand formation or as a line anchoring formation that could defend those in formation from all angles of attack, just as a standard shiltron. The way it was used was that the officer would shout "porcupine formation!" and the spearmen would put their polearms forward and form a circle, hence the name porcupine. Despite the fact that it had the support factor of a phalanx, the porcupine was far more similar to a standard shiltron than it was a phalanx.
The Shiltron is not mentioned by name in the Tolkien books and is only mentioned being used on The Lord of the Rings: The Battle for Middle-earth games and The Lord of the Rings Strategy Battle Game see:  (search Shiltron).
To read about how the shiltron affected the real world follow this link: shiltron.