From the moment he sits on that bus-stop bench and starts talking, Forrest is the narrator of his own movie. Yes, we see a few things that he couldn't possibly know, like Jenny wandering out onto a balcony while Forrest says, "I hoped that whatever she was doing made her happy." But these moments tend to be exceptions to the rule. Mostly (and unlike a box of chocolates), what you see is what you get.
The cool thing, though, is that the movie layers another perspective on top of Forrest's. As the audience, we get his perspective on events, but we also can use our superior smarts to figure out what's really going on in situations that go straight over sweet, dumb Forrest's head. That's narrative irony: when the audience knows something the character doesn't.
Sometimes, this contrast is funny or sort of cute, like when it comes to things like race and presidential honors. Sometimes, it's downright chilling, like when Forrest remembers Jenny's dad as "a very loving man."
Nice, right? Not when Forrest continues, "He was always kissing and touching her and her sisters." To Forrest, Mr. Curran is a nice guy who's fond of his daughters. To us, he's a criminal who's molesting Jenny and her sisters. From a narrative perspective, this is fundamentally ironic: we, the audience, know something that the character doesn't. That disjunction is classic irony.