To defeat the sixteen colossi in Shadow of the Colossus, Wander must reach and attack ornate, glowing symbols on their fur. These sigils are the "weakpoints" of the colossi, meant to contain the dark essences of Dormin within the sixteen beasts. Other weapons can damage these sigils, but only the sword can pierce them fully.
Sigils are always found on a colossus's fur - to attack them, Wander has to hang on with one hand (as the colossus will invariably be trying to throw him off) and stab with the other. A sigil usually takes about three well-charged stabs to destroy completely. Depending on the colossus and the difficulty level, there can be up to three sigils on its body.
The sigil design can also clearly be seen on the back of Wander's tunic, as well as the tunics of Lord Emon and his company. (A very similar design can also be found on Ico's clothes.) From this we can infer that the society, from where Wander and Emon have traveled, know about the nature of the magic that allows Dormin to be kept imprisoned. The stories circulating around this society, especially those concerning Dormin's ability to revive the dead, are likely what persuaded Wander to steal the sword and journey to the Forbidden Lands to ressurect Mono.