Human evolution is the evolution of options. By a wide margin, our species has the most options for responding to challenges. These options come at a great cost, but in the occasional moments when we use them, they catapult our fitness to great heights.
The Chicxulub asteroid filtered animals by temperature. In the immediate aftermath, large reptiles seared to death, whereas animals that could regulate their heat (i.e. "warm-blooded" mammals) burrowed and hid. Not only did they survive the immediate heat of the first couple days, but they survived the climate chaos that ensued. Mammalian metabolic innovations then laid the foundation for high-functioning brain modules due to greater oxygen exchange. These innovations are also shared by birds, who are descended from dinosaurs. While mammals dominate common rankings of the most intelligent species on Earth, those rankings often include a few birds, such as crows, parrots, and owls. There are no reptiles on these lists, though.
Appendages and physical degrees of freedom
In one sense, the primate form is similar to that of octopi. Our appendages are long relative to our bases: long fingers attached to short palms; long arms and legs attached to shorter torsos. Our limbs and digits, when spread out, resemble a nested or fractal hub-and-spoke, meaning that the freedom of our arms multiplies with the freedom of our fingers. The primates are gangly relative to other mammals. If one were to graph animals by the sum of their physical degrees of freedom, it would correlate to their intelligence. Elephants, for example, have the most dexterous of appendages: their trunks. (Dolphins are a great exception, though.)