A Dump Stat is roleplaying gamer slang for a character statistic with a less overall impact compared to the other characteristics. It is the opposite of a God Stat. Dump stats may be specific to a campaign (for example, an action-focused campaign where most interaction is of the fist-to-face variety will render a character's charming social skills mostly irrelevant), a GM's house rules, or can be present in the system RAW. Dump stats are often tied to a character's primary class or focus; combat-oriented characters tend to get little benefit from a high Charisma attribute, for example, whereas spellcasting classes who are usually expected to stay out of frontline combat likewise benefit little from having high Strength. Conversely, a dump stat could result from minimal penalties for having it low: a fighter can use other party members to do the talking for him (and paying hookers with gold negates bad social stats altogether), while a weak wizard can get a literal or metaphorical pack mule to carry things for him and not worry about the problems of having low Strength.
When a dump stat is obvious as a result of class selection or rules, if possible, many players will use it to ensure they have high scores in their important abilities (either by placing their lowest score in that stat or by neglecting to improve it in points-buy systems). Some consider this to be powergaming, but the practice is very widespread. No matter how you feel about the practice, it's hard to argue that players should be forced to spend finite resources on something that provides them radically lower benefits than anything else you can spend on. Some systems have made level up models which mitigate this a little, making additional points of high attributes more expensive, while low ones are very cheap, at least allowing players to spend left over experience, rather than the full rate for them. Unfortunately, this carries its own problems. A better system is probably attempting to make all stats important and useful for combat (which most games are built around); 7th Sea is a good example of such a system.
The traditional example is the Charisma ability score from Dungeons & Dragons 3rd Edition. All the other stats contribute some sort of primary or secondary gameplay or combat benefit beyond the skills associated with them: Strength decides melee ability and carrying capacity (with some impact on certain aspects of ranged combat), Dexterity adds to Armor Class, Reflex saving throws, and ranged ability (along with some forms of melee combat), Constitution grants extra hitpoints and bonuses to Fortitude saves, Intelligence gives out extra skill points, and Wisdom increases Will saves. Charisma only has an impact outside of skills checks when the DM says it does. Thus, unless the player wants to focus on having social skills or uses the attribute to cast spells, Charisma is always the stat that incurs the least penalties for dumping for any character.
Notably, both subsequent editions of the game reworked the stat system to make Charisma a more attractive choice for PCs, 4e by allowing either Wisdom or Charisma to improve Will defenses, 5e by attaching Charisma saves to a variety of nasty effects, including resisting possession, avoiding planar or dimensional displacement, and preventing life drain by various undead monsters.