DI stands for Directional Influence. It is useful for avoiding being KOed by strong attacks. You can use direction influence by holding the control stick diagonally up and in the opposite direction you are being launched horizontally in, or by holding it to the left left or right when being launched upwards.
Direction influence lessensslightly changes the distancedirection you travel whenin while being launched. This can allow(hopefully) allows you to not fly off the map, and hopefully recover via your B+up
move.