Definitions of "functional"

ENCODE: Something that changes a biochemical property of the cell [source]

PLOS Genetics: DNA shaping a person's body and behavior, i.e. phenotype [source]

Relationship between genes and features

Every feature existed for the first time in some ancestor. All of the features that define what it means to be human existed for the first time through billions of first-ancestors, going all the way back to LUCA (the last universal common ancestor), a small single-celled organism.

Intelligence is a feature. So is number-counting, even though number-counting is a form of intelligence. The word "feature" here is used instead of "trait" because trait commonly refers just to alleles, such as the eye-color alleles. In our terminology, blue eyes are a feature, just as the feature of having pigments are a feature, and just as having an iris. There was a first-ancestor with blue eyes, a first-ancestor with pigments in their iris, and a first-ancestor with an iris.

Einstein had a large helping of abstract thinking necessary to come up with the Theory of Relativity. He may have been the first-ancestor of just the size of his abstract thinking, or maybe someone further up the tree had that size. That size of abstract thinking may have shown up in someone else for whom their common ancestor may be many more generations behind Einstein's first ancestor who had that size of abstract thinking.

Here, we use the phrase "show up" as opposed to "evolve". Evolve connotates mutation and recombination. Mutations are very infrequent. Recombination has to be the main engine for new, polymorphic features. A highly polygenic feature, such as intelligence, "mutates" with every individual, producing brand new intelligences with every child. However, eye color is not very polygenic, and therefore eye-color evolution is indeed bound by genetic mutation.