Intelligence is traditionally the "brains" stat, or the "smarts" stat; it represents one's aptitude with reasoning, deduction and logic, as well as one's general state of education and openness to learning and study. The higher your Intelligence, the smarter and more educated you are. This makes it an important stat for an aspiring Skill Monkey, and in 3rd edition, it directly affected how many skill points you gained per level. Most Intelligence-related skills involve academic knowledge about various things in the fantasy world, from the mating habits of gnomes to the shortest route to the final boss. Primarily, and famously, it is used to identify monster weaknesses, defenses, and special attacks. It may also be of some aid in identifying that large, furry chap heading your party's way.
Ironically, whilst Intelligence is integral to the Wizard class, whose theme as a studied, educated spellcaster whose power comes from understanding the mechanics of magic itself, it's a popular dump stat for many other classes, especially fighters and other combat-orientated classes. This is because Intelligence usually doesn't have many direct applications to combat use in the tabletop, despite its important role in strategy, tactics, and identifying enemy weaknesses. Even in 5e, it's probably the safest dump stat in the game, though its saving throws are tied to a variety of psionic and mental effects that make up for their relative rarity with sheer nastiness.