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.
Charisma 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 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.
Because of its intended nature, Charisma is thusly one of the "mental" stats of D&D, which means 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.
It is one of the most popular dump stats in the six-score system for reasons explained on that page.