The image of God is a trinity, God, Jesus, Holy Spirit. By creating us in his image (not physical form, but characteristics) we were given everything we need, compassion, understanding, ability to think, etc. Verse 28 specifically mentions the ability to rule and subdue.
Through Jesus we are given that same authority. If we have an intimate relationship with him, we take on his character and have the power to change the world around us. Christ gave this authority to the Twelve in Matthew 10:1. This same authority is given to us. Mark 16:17-18, "And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues; They shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover."
"Verily, verily, I say unto you, He that believeth on me, the works that I do shall he do also; and greater works than these shall he do; because I go unto my Father" (John 14:12).
