What does Morph materia do?

The Morph materia makes your character perform an attack which generally causes very little damage to the enemy, but if this attack is used as a finishing blow on many monsters, they will "morph" into an item. (These items tend to be of higher quality than those stolen.)
The "Sense" materia may be necessary to gauge what time you should start using Morph on the enemy. Example: Enemy "X" has 2000Hp, and you wish to Morph a Power Source from "X". Your Morph only does 100 damage to an enemy, your normal physical attacks do 500. Attack "X" 3 times normally, (leaving "X" with only 500Hp) and keep using Morph (about 5 times) until "X" has no more Hp. "X" becomes a Power Source.
Morph usually only does 1/8 the damage of a regular attack, but Yuffie's ultimate weapon allows her to Morph with the strength of a regular attack...

It is interesting to know that Yuffie works the best with most of the Command Materia such as Steal Materia, Steal as Well Materia, Morph Materia and the like.

It will transform a Master Tonberry into a third ribbon .. Very useful