Combo Attacks are pre-set combo strings done by inputting a specific sequence of directions and/or attack buttons. These are different from normal combos as they are already pre-programmed. Some are also special move cancellable, making them very useful combo starters. They have very different properties per move in the sequence, effectively working as mix-ups and pressure sequences to keep your opponent guessing. As you may have noticed in the video below, the moves in between the strings are either mid, low, high, overhead, etc.
Sample:
I think that people who want to find combo moves should try testing pairs of buttons and see what happens with that character. The best place to this is in practice mode, where the opponent doesn't strike back!