As a human being you “have a mind” (unless you have “lost your mind”). But what is this intangible entity— mind? A word, first of all: a linguistic symbol for a concept of something intangible, invisible, but which seems essential to our being human.
“Mind” or “mentality” is our conscious awareness of the world we inhabit, extending to the cosmos at large. As our mentality is expanded and developed, we become more keenly and precisely aware of our circumstances in all respects—to the extent that the limits of our intelligence allow. We can only assume that much of reality extends beyond human ken and may never be comprehended by our sciences or intuitions.
But since there is wondrous much that human minds can grow to experience and understand, then aiming to do so to the fullest seems to be the implicit imperative of our mentality: minds must grow. And cultivating such growth, in all ways possible, is the mission of education, a word that etymologically implies both nourishing and drawing forth: the care and feeding of our human potentials latent and waiting to emerge.
“Higher education” would then intend to cultivate the higher reaches of human mentality. Why go to college? To grow your mind.