At the beginning of the movie, the other characters believe that he doesn't have any powers. It is only at the ending of the movie when they're displayed: distraught at being forcibly taken away from his mother, an infant Jack-Jack lashes out at a surprised Syndrome, who had kidnapped him (Jack-Jack's mother rescues him through a fastball special and parachutes him to the ground, while his father apparently kills Syndrome by using his own very expensive gull-winged sports car, Syndrome's cape, and the engine of Syndrome's private jet). Pixar also created the short film, Jack-Jack Attack that shows Jack-Jack discovering his powers while unleashing horror on his babysitter, Kari McKeen.
As Jack-Jack was at home during both the "Battle of Nomanisan" and Operation Kronos, he is the only member of the family who did not have any contact with Mirage. He usually dribbles baby gibberish and can barely speak in human form—he only did so three times in the movie: first, when Lucius Best/Frozone rang the doorbell to the Parrs' home (he says "Hello?"), the second, during his confrontation with Syndrome; he threatened in his many transformations (most notably his monster form), to kill the villain, all while throwing a tantrum he cries "Jack-Jack down!" the infant fought and scrambled down Syndrome's leg. And third, at the end when Helen rescued Jack-Jack after being dropped by Syndrome (he coos, "Mama!").
Jack-Jack normally communicates with subtle gestures and facial expressions.