The quick answer
Rune of Evolution turns eligible Exalted gear into Primordial Exalted gear. It randomly selects one T7 affix, upgrades it to T8 and moves it to a separate second sealed slot. It is different from Rune of Ascendance, which rolls a Unique or Set item.
Before using it
Check that the item has at least one T7 affix, is eligible for the craft and that you have the rune. Decide which ordinary crafts you want to complete first. Place it in the Forge, select Evolution and read the actual preview and cost before executing.
With several T7 affixes, you cannot guarantee which one becomes T8. A successful result is marked Primordial and has the T8 affix in its separate slot; that sealed affix is not an ordinary shard-upgrade target.
Cost and equipment limits
In 1.5, the maximum FP cost is 15. This does not mean every use costs exactly 15 or that the item must have exactly 15 FP. Read the Forge preview for eligibility.
Only one Primordial item of any kind can be equipped at a time. Consider which equipped Primordial item this would replace before committing a valuable base. Legendary compatibility is not covered here.