This doctrine is theologically deep and consequential, and is made the basis of all sorts of important concepts regarding the nature of man, theological ethics, the relationship between man and God, etc.—as well as the basis of heresies. But, I will keep this answer brief. The Hebrew words suggest we are made in God’s “image” or form, “after our likeness” or similitude or model. We are in God’s likeness—the imago dei—but how? John (4:24) writes that “God is a Spirit” or, as more recent translations have it, “God is spirit.” The Spirit of God is mentioned as early as Gen 1:2 in the Bible, and in many other places thereafter. Hence it seems likely that the claim that we are made in the image or form of God is to say that our spirits, or souls, or minds, or characters were made in some fashion like God’s. It is not hard to find ways in which this might be true: God is represented as having a free will, with the ability to make plans and form purposes, as we do; of having a mind, thoughts, and reasons, as we do; and of having assorted emotions, including love and anger, as we do. Moreover, in the same sentence, God says he would give man dominion over other living beings; so a common suggestion is that we resemble God in that we have this “dominion,” although in a much narrower domain. Finally, we are also supposed to be like God in that we are can be evaluated morally, as righteous or sinful. Of course, since God is perfectly righteous, it follows that in Adam’s fall, man’s nature became less like God’s, insofar as man became sinful; so also, in our ultimate redemption and rebirth, according to the New Testament, the imago dei in us will be more fully restored.