One characteristic that humans clearly possess that animals do not is one that we tend to take for granted, namely, an ability to use mathematics. Whether or not some animal species may have some capacity for performing some very basic mathematical functions like counting, the fact remains that animals lack an ability to understand and use advanced mathematics. On the other hand, it was the human ability to use advanced mathematics that allowed a great scientist like Sir Isaac Newton (1643-1727) to demonstrate "that the entire universe is a single uniform system, describable everywhere by the same mathematical laws" (Nancy R. Pearcey and Charles B. Thaxton, The Soul of Science: Christian Faith and Natural Philosophy, p. 129). In fact, the celebrated naturalist Alfred Russel Wallace (1823-1913), usually described as the co-discoverer of evolution along with Charles Darwin, was convinced that a capacity for mathematics marked humans as unique. In a 1910 newspaper interview (see here), Wallace asserted "The difference between man and the other animals is unbridgeable. Mathematics alone is sufficient to prove in man the possession of a faculty unexistent [sic] in other creatures."
Another characteristic that humans exhibit and animals do not is an ability to use language. Some try to argue that forms of communication used by certain animal species are analogous to human language, but this is not really true. As philosopher J.P. Moreland points out, one reason for the claim that animals do not possess language is that there is a "lack in animals of grammatical creativity and logical thought about language itself that is present in real language users [i.e., humans]" (The Soul: How We Know It's Real and Why It Matters, p. 144). Moreland also argues that animals lack language because they lack an ability to use symbols, and a capacity to use symbols is essential to "real language." Indeed, unsuccessful efforts by researchers to teach animals to use language would seem to support the assertion that animals do not possess language.
In contrast, human beings seem to be "hard-wired" to acquire and use language, and this is clearly demonstrated by some recent research. In a blogpost at Mind Matters, Denyse O'Leary reports on a recent study that found "evidence that, when a child hears speech before birth, the complex neurological processes that enable early acquisition of language are stimulated." In the study, reported in Science Advances, researchers exposed a number of newborns whose mothers were native French speakers to "Goldilocks and the Three Bears" in Spanish, English, and French. The newborns were then monitored for neural activity. As O'Leary notes:
If [the newborns] heard French last, their brain oscillations correlated with speech perception and processing showed greater activity. It appeared they were already primed to start interpreting French from their prenatal experience of hearing their mothers'--and perhaps others'--voices.
Thus, it would seem that a capacity for learning (and ultimately using) language is present in humans at a very early stage of their development. Animals, however, do not exhibit such a capacity.
In short, given that humans possess abilities to use mathematics and language, which animals do not, it is clear that humans are far more than highly evolved animals. As for where they acquired such sophisticated abilities, it is not--it would seem to me, at least--unreasonable to suppose that they are not the gifts of a process of blind evolution, but of a Creator, who made them in His image.
Image of Sir Isaac Newton from Wikimedia Commons