First of all, it's spelled "dimensions". If God is a spirit, and we are physical humans, then we are not exact duplicates, which the words "image" and "likeness" refers to. Being in the image and likeness of God would mean then that we have qualities like him, much more so than any animal can have.
This means things like love, justice, wisdom, power, along with the one thing that no other creature has: free will. Animals act on instinct, but humans have the ability to reason and think for themselves.