Let's give a somewhat more useful answer already:
The point of saying "you should look at your opponent, not your own character" is obviously about one thing: The stuff your character does, doesn't require constant supervision. You have him somewhere in your field of view (it's a TV not a cinema screen after all), which is usually enough... if not practice more, and while you haven't reached that point, try to get by with quick glances.
Because there is something that does require constant supervision: your opponent. He is the most dangerous thing on the stage after all, and the least predictable one (well, and if he IS indeed more predictable than the movement of Randall, then you're probably winning by a landslide either way haha). How do you even choose what move to beat what he is doing, if you don't know that?
He should also be the main focus of your thought process as well. Thinking about what you want to do next, should rarely if ever be "I am Falco, I want to shoot a laser", but more "My opponent is dash dancing over there, I want him to stop that. He can't punish me right now, if I shoot a laser, so that's what I'll do".