Dynamite are Key Items in Xenoblade Chronicles. They can be found in the Ether Mine. There are three of them, and they must be obtained for Making a New Path in Colony 6. When they are delivered to Gorman, he will use them to blow open a new path at Spiral Valley on Bionis' Leg, making it possible to complete For the Restoration without defeating the monster blocking the path.
On the Ether Mine map: