Of the six stats, Charisma is the "Social" stat; its traditional use is to govern interactions with NPCs - the higher your Charisma, the better your chance of appealing to them or manipulating their emotions. Skills like Persuasion, Bluff, Intimidate, Deception, Diplomacy and so forth may cover direct skill at eliciting the desired result over the various editions, but they all key off of your Charisma, and a low Charisma makes you suffer penalties to succeeding, just as a high Charisma increases your chance of success. It's also been (belatedly) recognised as the Alpha Male stat - correlated with sheer willpower. One of the things 4th Edition did (arguably) right was to suggest CHA for a bonus to Will saves, rather than WIS.
Because of its intended nature, Charisma is thusly one of the "mental" stats of D&D.
CHA should come into its own in wargaming, which BATTLESYSTEM recognised. If only more gamers played it. Also, as a mental stat, it's used as a power source for certain spellcasting creatures or classes. Charisma-based spellcraft tends to reflect instinctive or inherent magical abilities; the caster doesn't study hard (Int) or use mental discipline and faith (WIS) for their power, it comes from within and is directed by sheer will.
The iconic Charisma-based class in D&D is the Bard. He turned out to be annoying so later we got the Sorcerer (as of 3rd edition), an inexhaustible source of skub. Both were frequently ruled out of d20 settings and/or tweaked into unrecognisability. 4e floated the Warlock. Here and there is the Paladin, if one focuses on the latter's gish status.
Charisma is most infamous for its unpopularity: it is the most common dump stat in the six-score system, especially in Third Edition. Even if you're not playing a melee martial class, or using strength-based skills like climb and swim, strength is still useful for lifting and smashing stuff. Even if you're not playing a Ranger or Rogue, or using dex-based skills like balance and hide, dexterity still helps with initiative, armor, and reflex saves. Not making Concentration checks often? Constitution still boosts hit points and fortitude saves. Not a wizard or psion? Intelligence still increases your bonus languages known and skill points earned per level. Not a divine caster or making a spot/listen check? Wisdom still boosts will saves. But charisma? Charisma doesn't do a goddamn fucking thing unless your class says so or you're using a skill that keys off of it. Other editions have similar problems, but Third Edition assigning secondary functions to every other stat (and making the bonuses from high stats and penalties for low stats linear rather than concentrated at the ends) exacerbated them. Notably, both successive editions made changes to make Charisma a more-attractive choices of stat focus.
CHA also suffers from a rather contradictory nature in that it's never been quite clear what it's supposed to come from. Most people tend to assume it relates to physical looks; after all, NPCs with high charisma tend to be depicted as gorgeous (for example, nymphs), whilst low charisma races tend to be ugly and monstrous (orcs, ogres, etc). However, D&D has always claimed that Charisma is more of a strong personality and "natural presence" than anything directly relating to beauty, with many dangerous but imposing monsters having high Charisma and ugly looks, such as dragons, aboleths, and mind flayers.
In fact, Gygax himself tried to address this, introducing the never-took-off seventh ability score, Comeliness, in Dragon Magazine #67 specifically to create a separate "beauty stat". It... didn't work out so well. Neither did subsequent attempts.