Directional influence, abbreviated DI, is the control the receiver of an attack has over his or her trajectory. Each attack sends its target in a particular direction, depending on the attack itself and on the target’s weight and falling speed; DI can be used to alter, but not completely change, this original trajectory.

Wiki: http://www.ssbwiki.com/Directional_influence
My SC: https://www.youtube.com/watch?v=UIdyVK1aDtg
BSD: https://www.youtube.com/watch?v=MH_46_2BtOM

Combo DI in action! https://youtu.be/uNO5FudmyAc?t=250