Amplifying Emblems are used to upgrade Signature Items from level 11 to level 20. 70 Emblems in total are needed to upgrade Signature Item to level 15, and 240 Emblems in total to upgrade it to level 20.
Amplifying Emblems are less common than Primordial Emblems, and acquiring them can be quite expensive. They can be obtained from currently ongoing Tavern Bargains event, higher King's Tower floors, gift sets, other events and AFK Rewards starting from Chapter 18. They can be also bought from the Store for diamonds.