"Then God said, 'Let us make mankind in our image, in our likeness, so that they may rule over the fish in the sea and the birds in the sky, over the livestock and all the wild animals, and over all the creatures that move along the ground.' So God created mankind in his own image, in the image of God he created them; male and female he created them." - Genesis 1:26-27
The Bible teaches that human beings were made "In God's image" in the creation account in the book of Genesis. The Bible doesn't say anywhere else that any other creature bears God's image. This seems to be a property that only human beings have. Only human beings are made in God's image. However, what exactly does it mean to be "made in God's image"? It can't mean that we look like God. After all, everyone in the world looks different from one another (with the exception of identical twins, triplets, etc.). Moreover, God is an immaterial being and therefore is invisible (John 4:24, Colossians 1:15). So He doesn't really "look" like anything. God is an immaterial being and therefore doesn't have photons constantly bouncing off of Him. This is an exception in the incarnation of Jesus however (John 1:14), but even then, it's only His human nature that is visible, not His divine nature. This is why Colossians calls Jesus "the visible image of the invisible God." (1:15).
Therefore, it's reasonable to infer that the imageo dei (Latin for "image of God) has nothing to do with our physical bodies. It is most likely that the imageo dei refers to certain properties of the human mind. These would be properties that no other creature on Earth possesses but which God does, and which He imbued to humanity. What are those properties?
One mental property that sets God and man apart from all other animals is that man is a rational creature. Man can reason "If P, then Q. P. Therefore, Q" or "Either P, Q, or R. Not P or Q. Therefore, R." Man can do mathematical equations. Man can discern the laws of logic such as the law of non-contradiction, for example. He knows that the truth cannot be both A and non-A at the same time and in the same sense. Animals do not possess reason. I highly doubt that my dog Max has ever made a deduction from known facts, or used any of the 9 logical rules of inference, for that matter, to draw a conclusion. This is why he can't figure out that thunder and fireworks aren't something to be afraid of. If he were rational, he'd probably come to that conclusion by some argument like "If my humans aren't freaking out, it's probably nothing to be alarmed over. My humans aren't freaking out. Therefore, there's nothing to be alarmed over." He doesn't possess the rational faculties needed to take those steps needed to reach that conclusion.
2: A Knowledge Of Good And Evil
Man is also aware of the existence of objective morality. Unlike animals, we know that certain things are morally right and others are morally wrong. Humans have the moral law written on our hearts. Romans 2:14-15 says "Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them."
Human beings are moral agents, knowing right from wrong and being able to choose right from wrong. Animals, by contrast, are not moral agents. They don't know the difference between good and evil. This is why The Bible makes no mention of animals standing before the judgment seat of God to be judged according to what they have done (Revelation 20:12). The Bible nowhere mentions God holding animals accountable for sin. This is because they are not moral agents. This is also why we don't preach the gospel to our pets. They don't need a Savior because they're not guilty of any sins.
3: Free Will
Free Will is one more aspect of the human mind which separates us from the animals. Animals are ruled by their primal instincts and they can't do anything but follow those instincts. Human beings, however, can choose to go against their instincts and act contrary to their nature just by sheer volition. A Lion cannot just up and choose to become a vegetarian one day. He can't decide "You know what? Killing Gazelles is getting pretty old. I feel sorry for them for one thing. For another, it's tiring to chase after them day after day. I'm going to stick to a fruits and veggies only diet". A lion cannot do that because a lion doesn't possess free will. He can only act according to his nature. Humans can decide what kind of diet they'll have. Some decide to be vegans, other carnivores, and others are omnivores (i.e meats and veggies). However, non-human animals are what they are. If they're carnivores, they're carnivores, and they could never decide to change that.
The Implications This Has For The Origins Debate
Given all that I've said, I'd like to mention the implications that this has for the creation/evolution debate. Many Christians oppose Darwinian Evolution because they think it undermines the imageo dei. If evolution is true, they say, then man is nothing more than a highly modified ape. He's a big monkey in a suit. Likewise, I sometimes hear Christians object when scientists say "We are literally star dust" in reference to the fact that all of the elements that comprise our bodies originated in the furnaces of stars over billions of years. I've heard some say "I'm not star dust! I'm made in God's image!"
But the thing is, if the imageo dei is grounded in our mental qualities, those qualities which belong to our spirits, rather than to our physical bodies, then it doesn't really matter how our physical bodies originated, does it? Maybe the Darwinists are right. Maybe we are modified monkeys. But if our spirits are made in God's image (i.e bearing rationality, the moral law, free will), then we're modified monkeys, but we're not merely modified monkeys. We're hominid creatures that bear the image of the Creator God. And therefore, humankind isn't on the same ontological level as chimps, cockroaches, beavers, and everything else. If God created us (through evolution in this scenario), then even though we evolved from lower apes, we are still ontologically greater than all other creatures on the planet, for it's our spirits that set us apart from the rest of creation, not our bodies.
We may be evolved apes, but we're more than evolved apes. We are literally star dust, but we're more than star dust. The church has always taught that the human person is more than the physical parts which comprise him. Since the imageo dei is grounded in our mental faculties, how the human body came into being is irrelevant. So whether you believe man evolved, or whether the first humans were created miraculously and spontaneously, it has no implications for the divine image either way.