The idea is, to someone who lives in a standard D&D world, even if they cannot use magic, they understand what magic is to a degree. Wizards and Clerics use very similar magical techniques, even if what spells they cast can differ.
Psionics are different and strange and follow completely unknown rules. They evoke wonder, awe, and fear in a fantastical setting where the wondrous is more commonplace.
They stand out in a D&D world the same way a spellcaster would stand out in our world. Psionics was added to AD&D because the people who made the game loved weird pulp fantasy, with alien monsters, bizarre powers of the mind, and lost civilizations with advanced technology indistinguishable but different from magic; all existing alongside fighting men with swords and finger wiggling magic-users.
The people who love psionics think of it as a spice, I imagine. A way to add an element of the otherwise to the standard fantasy game. Traditional D&D characters are supposed to look at psionics, monks, binders, malconvokers, shadowmages, truenamers, soulmelds, martial initiates, spellfire wielders, and the like and go "how in the Nine Hells did you do that?"
And that dash of mystery can make the game much more fun for some, as opposed to "oh look, he cast a fireball. How creative of him. Ok, everyone stand apart so we don't get hit by the blast pattern, you know the drill, guys."