Heh. This is a question that is made more interesting by contrasting BOTH of my MC's, instead of just talking about Adi. Because Adi and Koreal are both very smart, but in different ways.
Koreal is a wizard. He is very, very intelligent. He's highly educated, and has committed to heart and soul (and flesh and bone...) the inner workings of the world in order to perform magic. He speaks and reads dozens of languages, and if he were a character in a modern-day setting, he'd be something like an astronomer, a mathematician, a lead programmer, or more likely some combination of those.
...but he isn't always great with people. He's sometimes bad at reading between the lines, picking up on social white lies, or understanding another person's point of view, or why they'd do something the way they do. This produces plenty of misunderstandings, hurt feelings, and arguments. He can understand the inner workings of the cosmos... but not why someone would lie and not just straight up tell him his shirt is ugly.
Adi, in contrast, did not have Koreal's extensive education. Don't ask her to do complex math, or expound on classic literature, or explain how weather works. Magic is right out. She speaks a small handful of languages, mostly those that a traveler would commonly encounter. She's not fluent in all of them. She sometimes feels really dumb around Koreal...
... until she sees him flub what should have been a really simple, obvious social interaction. What Adi lacks in book smarts, she has in spades when it comes to reading people. Her instincts for subtle cues, hidden intentions, and other people's perspectives are very, very good. She's a good judge of character, which is an important skill to have if you sometimes have to make snap judgments about who to trust. I'd say it's because of all the traveling she does, and the many, many people she's met, but Koreal has done just as much adventuring, so it's really something she was born with.
And then both of them have great situational intelligence (aka knowing when a situation is about to go straight to Hell in a handbasket, and that it's time to get out of there), but that particular form of street smarts was earned.
Summary