Intelligence (abbreviated INT) is a statistic that in earlier games affects the use of Intelligence-Type Techniques. If your monster has high intelligence, these types of attacks damage an opponent more. These include using magic and mind attacks like illusions, telekinesis, or telepathy. Also, a monster with high Intelligence receives less damage from an INT-Type Technique.
In later games, intelligence is used to effect how a monster responds to your commands. An un-intelligent monster will easily get confused in battle and will be an easy target for its opponent since it cannot attack or defend itself. High Intelligence also aids in searching for rare items during adventures. In Monster Rancher DS, it is taken a step further and the intelligence stat determines if your monster will obey your commands on explorations.