Aoki ducks under an opponent and then lunges upwards with a powerful uppercut. The motion of the punch mimics that of a leaping frog. Aoki also uses his Frog Punch as a follow-up after using the Look Away.
Despite being a running gag throughout the series, the Frog Punch is in fact a dangerous technique, as the momentum of the leap can add tremendous value to the punch. A more appropriate application of this momentum can be seen in the Gazelle Punch, however, which uses jumping momentum, but doesn't require going airborne and has longer reach and quicker execution.
These are all glaring weakness of the Frog Punch: it cannot be used outside of close range, the wind up is obvious to anyone who's seen it before, and at the same time one cannot afford to miss with it. It is easy to counter, as the trajectory is predictable.