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 (GMs who cleave to the "roleplaying not rollplaying" defense often make social skills totally redundant, calling every social encounter entirely based on the player's acting and word choice rather than asking for or allowing social skill rolls and letting the character be better than the player at something), 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, allowing and incentivizing players to spend left over experience to improve them on the cheap, rather than making them directly give up improving their "core" stats. Unfortunately, this carries its own problems.
A better system is probably attempting to make all stats important and useful for the core mechanics the game is built around (which for most games means combat). Look to 7th Sea for a good example of such a system. Since all five stats have a direct impact on combat, dumping any one of them causes harsh, punishing penalties; virtually every new player is advised to buy every stat up to at least two, and most veterans do the same for all but the most gimmicky of characters.
The traditional example is the Charisma ability score from Dungeons & Dragons. 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, Initiative checks, 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. In classic 1970s-era D&D Charisma only had an impact outside of its associated skills checks when the DM says it does. In those "core" rules, unless the player wants to focus on having social skills or has class features that use the attribute, such as spellcasting, Charisma is always the stat that incurs the least penalties for dumping for any character.
This was realised very early on, so several attempts were floated to give high-CHA players something to do. AD&D floated the Bard... LOL. Then came the Companion Set's War Machine and BATTLESYSTEM, where CHA was actually something of a God Stat, if only wargaming was something the party wanted to play. Then Third Edition proposed the Sorcerer, if only the Sorcerer was something that wasn't totally broken.
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 and the Power system making it a direct component of many character classes' combat ability, 5e by attaching Charisma saves to a variety of comparatively rare but deeply nasty effects, including resisting possession by outsiders and ghosts, avoiding planar or dimensional displacement, and preventing life drain by various undead monsters.
If we're looking for a cautionary-tale on what happens if you dump-stat the wrong thing and then go to the wrong place: X12: Skarda's Mirror. Whether it was Mallek's WIS 13 or his CHA 15, it wasn't enough against the last thoughts of a dying god.