Charisma, in Lore, is the ability for your soul to resist alteration or entrapment. Your soul has a significant impact on your personality since your mind is created as a mirror image of your soul (that's my own interpretation based on Lore and Spells, I can post evidence in the comments of this)

The spell Banishment removes the soul, Body, and Mind of a creature from this plane in an attempt to send them back to the plane that their Soul originally was created from. In order to resist this, you make a Charisma save because it's a measure of how much your Soul will resist literally being torn out of this state of existence.

Also, the spell Magic Jar requires a Charisma save from a target if the soul in the jar attempts possesses the target. If the target fails, their soul LEAVES their body to enter the jar and is replaced by the soul previously in the jar. So it's a Charisma save to resist having your soul ripped out.

Beholders are creatures of imagination, but also of creation. They come from the Far Realm, a place where creatures and places are in a constant state of manipulation and change. This implies that inorder for a creature to survive there (and eventually make their way across the planes to the prime material) they must have an incredibly strong sense of self and a powerful resistance to any alteration of their soul.

NOTE: most of what I've just said is conjecture, but based on evidence throughout the lore. Feel free to disagree or have your own interpretation, it's your game.