In the Insight on the Scriptures (published by the Watchtower Society), the article on the word Image says the following:
Whereas references to images in the Bible frequently relate to idolatry, this is not always the case. God, in creating man, said first, “Let us make man in our image [or, shadow, semblance], according to our likeness.” (Ge 1:26, 27, ftn) Since God’s Son stated that his Father is “a Spirit,” this rules out any physical likeness between God and man. (Joh 4:24) Rather, man has qualities reflecting, or mirroring, those of his heavenly Maker, qualities that positively distinguish man from the animal creation. (See ADAM No. 1.) Though in the image of his Creator, man was not made to be an object of worship, or veneration.
Even as Adam’s own son Seth (born to him in his imperfection, however) was in Adam’s “likeness, in his image” (Ge 5:3), Adam’s likeness to God originally identified him as God’s earthly son. (Lu 3:38) Despite man’s fall to imperfection, the fact of mankind’s originally having been made in God’s image was cited after the Noachian Flood as the basis for the divine law authorizing humans to serve as executioners in putting murderers to death. (Ge 9:5, 6; see AVENGER OF BLOOD.) In Christian instructions concerning feminine head covering, Christian men were told they ought not to wear such a covering, since the man “is God’s image and glory,” while the woman is man’s glory.—1Co 11:7.
Ellicott's Commentary for English Readers under Genesis 1:26, gives us similar insight:
In our image, after our likeness.—The human body is after God’s image only as being the means whereby man attains to dominion: for dominion is God’s attribute, inasmuch as He is sole Lord. Man’s body, therefore, as that of one who rules, is erect, and endowed with speech, that he may give the word of command. The soul is first, in God’s image. This, as suggesting an external likeness, may refer to man’s reason, free-will, self-consciousness, and so on. But it is, secondly, in God’s likeness, which implies something closer and more inward. It refers to man’s moral powers, and especially to his capacity of attaining unto holiness. Now man has lost neither of these two. (Comp. Genesis 9:6; 1Corinthians 11:7; James 3:9.) Both were weakened and defiled by the fall, but were still retained in a greater or less degree. In the man Christ Jesus both were perfect; and fallen man, when new-created in Christ, attains actually to that perfection which was his only potentially at his first creation, and to which Adam never did attain.
So being made in God's image and/or likeness is to be understood as having similar qualities and capacities as the Creator, but not to the same degree.
Man's likeness to God can also be seen in his governance over the earth as is illustrated in the Awake! December '88 article What Does Genesis Really Say?
Another description of the creation of man is found at Genesis 1:26. There God says: “Let us make man in our image, according to our likeness, and let them have in subjection the fish of the sea and the flying creatures of the heavens and the domestic animals and all the earth and every moving animal that is moving upon the earth.” (Genesis 1:26) Since the Bible tells us that God is a spirit, the phrase “in our image” must be understood to mean possessing God’s qualities.
This statement explains, in a way that evolution never could, why man is so different from the animals. Only man can control the animals and the vegetation around him. Only man has a moral sense and a conscience. Only man has a wide freedom of choice and such a developed intelligence. Only man has the ability to conceive of the existence of God and the gift of speech with which to speak to Him. The Journal of Semitic Studies says: “Human speech is a secret; it is a divine gift.”