The simplest plot involves a hero progressing from one situation to the next in a linear progression. Like a detective moving on from the crime scene to one suspect and on to another, the hero's decisions may have no real bearing on how the story unfolds, until the climax when the villain is revealed.
Not that there's anything at all wrong with this kind of story. I'm a great lover of detective stories and crime procedurals.
Some heroes, though, push things a little too far. They're not happy to let the world move around them. Instead, they move the world. They kick in doors and get in people's faces. They make mistakes, win surprising victories, and the results of that can change the course of a story or even reverberate throughout the remainder of a series.
It's always great to be able to see how one character's decisions alter the course of the narrative. It makes the setting seem vibrant and alive, like there's more to it that just our POV character(s). Of course, the most immediately obvious form of consequence is when the hero screws up. They lose a lover, a friend dies, they get arrested. These are awesome. Heroes should never glide through the story unscathed. I want to see what they stand to lose if their fail, and I want to know that there's a very real chance of that loss happening. Even more, I want to see the consequences of the sacrifices the hero is willing to make. Does he break the law to catch the bad guy? Does he have to go to jail or start hiding from the police as a result?
But there's another kind of consequence that's just as important, and often even more fun to experience. It's when the hero takes charge of his environment and starts changing it with his very presence, hopefully for the better. No longer is the hero reacting to events and struggling to persevere. Now he is becoming a force of nature in and of himself. He kills the villain, and when we next meet the hero in the series, he is loved by the authorities and reviled by his enemies. Maybe he's being targeted by vengeful hitmen, or been given new responsibilities by the authorities that help him do more good, but mean that he has to sacrifice more of his personal life.
Consequences give life to a story. They are raw material writers can use to let their world grow from the seed of an idea into a breathing, emergent creature that has to be fed and nurtured.