First of all, the Spiritual Stones are the magical objects that let you take the Master Sword from its pedestal. This idea is taken from OoT, but it's almost the same also in LttP, just with amulets. Collecting them is like a trial to see if you are worthy to get the Master Sword.
Now, after you have the Master Sword, you need to go to the northest part of Death Mountain. First reach the area full of crystals (you can latch onto the gray ones), then superbomb the white fence.