Abarim Publications' online Biblical Hebrew Dictionary
The verb טבע (taba') means to impress or sink down. It's used to describe how David's slung stone became lodged in Goliath's forehead (1 Samuel 17:49), but also how Jeremiah sank into the mud at the bottom of the cistern that became his prison (Jeremiah 38:6, 38:22, see Psalm 69:3, 69:15 and 9:15), or how the gates of the daughter of Zion sank into the ground (Lamentations 2:9), or how Pharaoh and his army sank into the Sea of Reeds (Exodus 15:4).
Judging from its derivation, this verb was also used to describe the sinking of a signet-ring into wax, and via that usage our verb appears to have contracted a secondary meaning of being established or decreed. Hence YHWH challenged Job to declare on what the foundations of the earth were sunk, or perhaps via which decree the earth was made to come into existence (Job 38:6). Likewise, Hochma (wisdom personified) declares that before the mountains were sunk (or perhaps established by decree), she existed (Proverbs 8:25).
The sole derivation of this verb is the feminine noun טבעת (tabba'at), meaning ring, but where our English word "ring" brings to mind something round, the Hebrew word טבעת (tabba'at) brings to mind something used for placing a mark in wax on some document and thus to authorize a document and to secure and uphold its content. This noun is used for the signet-ring of Egypt's Pharaoh and his viceroy Joseph (Genesis 41:42), and Persia's king and his crony Haman, later Mordecai (Esther 3:10, 8:2).
Doubtlessly, because of the power these sign-mark devices represented, they were mounted on rings so that the king or his official could conspicuously wear them in a perpetual demonstration of who had the power in a symbolic way, and where the ring was in a practical one. In other words: ring-bearers were power-bearers, and handing one's ring to someone was giving that person one's power (hence the wedding ring, by the way).
It appears that in Moses' time the ring had already become a common ornament (Exodus 35:22, Numbers 31:50, also see Isaiah 3:21), but the ring's use in the tabernacle complex clearly demands an exegesis beyond the mere practical (Exodus 25:12 to 39:21).