"To me, who am less than the least of all the saints, this grace was given, that I should preach among the Gentiles the unsearchable riches of Christ, and to make all see what is the fellowship of the mystery, which from the beginning of the ages has been hidden in God who created all things through Jesus Christ; to the intent that now the manifold wisdom of God might be made known by the church to the principalities and powers in the heavenly places, according to the eternal purpose which He accomplished in Christ Jesus our Lord, in whom we have boldness and access with confidence through faith in Him" (Ephesians 3:8-12).
The principalities and powers refer to the spiritual beings we see mentioned periodically, such as cherubim, seraphim, and angels. "For by Him all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him" (Colossians 1:16).
What Paul is stating is that God's wisdom is on display through the agency of the church. In seeing the church, these principalities and powers see the plans God had kept hidden through the ages.
Paul is not stating that the church teaches the spiritual realm. However, the church is involved in a battle against at least some of these beings. The phrase "principalities and powers" can refer to those spiritual being who have arrayed themselves against God. "Having disarmed principalities and powers, He made a public spectacle of them, triumphing over them in it" (Colossians 2:15). And that battle continues. "For we do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this age, against spiritual hosts of wickedness in the heavenly places" (Ephesians 6:12).
That God effected a plan to save the world through the church caught the host of evil off guard. It wasn't what they imagined -- or they would have moved to have blocked it. "However, we speak wisdom among those who are mature, yet not the wisdom of this age, nor of the rulers of this age, who are coming to nothing. But we speak the wisdom of God in a mystery, the hidden wisdom which God ordained before the ages for our glory, which none of the rulers of this age knew; for had they known, they would not have crucified the Lord of glory. But as it is written: Eye has not seen, nor ear heard, nor have entered into the heart of man the things which God has prepared for those who love Him"" (I Corinthians 2:6-9). Yet, in seeing it revealed, they are forced to admit the wisdom of God in saving men in this manner.