I can confirm that Solomon is the name of an ancient king and famed summoner and binder of demons - his ring and seal captured even Asmodeus, who at the time was considered the strongest of all demons (even if she's actually kind of a brat) and his writings form the basis for all modern demonology. His magical power made the ancient kingdom of Israel the wealthiest and most poweful nation in the world before he was eventually cast down for his hubris and idolatry.

Based on context, he may be just a namesake for this Ring, but given that the magic here purportedly relies on spirits very similar to demons, my guess would be that it's some means of controlling the Spirits and those the Empower.