The Hyperion thread adapter is needed to attach a barrel with a smaller (thinner) diameter than 0.735", and allows the barrel to be threaded into the Hyperion and Hyperion K suppressors from CGS Group. The Hyperion family of suppressors can be direct threaded onto a 5/8"x24 threaded barrel of normal diameter, but if the barrel is thin, the adapter is need to seat the barrel into the Hyperion suppressor.
The thread adapter can also be used with normal thickness barrels, adds a certain amount of muzzle gas diffusion and acts as a break and flash suppressor. The thread adapter is also helpful in sealing the connection of the suppressor, as the taper in the thread adapter allows for more complete locking. Near the base of the thread adapter is a flat area to accept a deep socket, box wrench or possibly a 12-point wrench.
For a review of the suppressor and comments on the thread protector see: Review of Hyperion Suppress and Thread Protector in The Truth About Guns
Picture credit: CGS Group and The Truth About Guns