IQ is a stat in the Mother series, short for intelligence quotient. Its effect is not entirely clear, as it is not described in-game. However, in EarthBound, IQ increases the amount of PP you have, an IQ point is equivalent to 5 PP, also, Jeff Andonuts' IQ affects his ability to fix broken items. Also, some PSI, such as Brainshock, can be affected by the IQ level of the attack target. The IQ stat also increases the chance to not fall for the New Age Retro Hippie's Bullhorn.
In the Mother 3 hidden memo menu (found by holding the L and R buttons while entering the status menu) available in the fan translation patch, it is explained that "If a character is able to use PSI, a higher IQ will increase its effectiveness."