You are asking about this familiar passage from Genesis (1:26): "Then God said, 'Let us make man in our image, after our likeness; and let them have dominion over the fish of the sea, and over the birds of the air, and over the cattle, and over all the earth, and over every creeping thing that creeps upon the earth.'"
This is from the first of the two distinct and different versions of creation that open the Book of Genesis—the "Priestly Version," written around the time of the return from Babylonian exile. It defines the seven "days" of creation, which metaphysically represent the seven stages of the creative process through which the Allness of God is focused and defined in the realm of Divine Ideas. (We use the same process as the Law of Attraction as we continue the creation by bringing our own thoughts and beliefs into tangible expression.)
In this version, man is the culmination of the process, created on the sixth day and given "dominion" over everything "on all the earth" that had been created to that point. Uniquely in all of creation, mankind is created "in our image, after our likeness." (It's an interesting and open question whether there's a committee at work here, or whether God is using the "royal" we.) At this point there has been no description of an image or likeness of God—nor will there ever be in the pages of the Bible. So what does this mean?
All we know of God to this point is that God is Spirit, the Power that begins in chaos, moves upon the waters and chooses to create expressions of Itself. That is the image we are given—a power of infinite creative possibility, a rich appreciation for the good and a loving concern for the expressions of life as they are created. That, then, is the unique "likeness" to God that we are. We are created as Spirit, creative, discerning and loving. The word "dominion" doesn't mean authority and control, but rather implies a sense of responsibility. We are created to be the Allness of Good in immediate expression, enfolding creation in the energy of goodness and love that we are.