An example of a scene's hard cut might go like this; character A says to character B, “I never get in a fight." Then we hard cut to a shot of character A getting punched in the face. It’s dramatic, and it can be comedic as well.
Maybe this switch doesn’t sound like a big deal. That’s because in film making, editing is made to be ignored when watching a film. Match cuts, dissolves, and all of the standard techniques are made to not be noticed. When you are watching a scene of two people talking you aren’t thinking about the fact that angle changes each time one of the characters begins to speak. You don’t think about how it cut to a close up as the scene became more intense. That’s the point.
Hard cuts demand your attention because they startle you. Where did that guy’s face go? Why am I staring at grass now?
Another kind of hard cut is the abrupt cut to black screen. Sometimes with some kind of chapter-like title or maybe the title of the film. The film Dallas Buyers Club used this to great effect as they tracked the main characters supposed 30 day life span. He would pass out on the floor and then hard cut to a black screen saying ‘day 4.’
It was an effective trick because it did not allow you to linger on the previous moment and forced you as an audience member to focus on that number.
So here are some examples of hard cuts(Due to the limitations of Youtube this is the best I could find).
This scene from Slumdog Millionaire uses jump cuts for the initial establishing of three different locations over the course of this scene and at the very end there is one final jump cut to a flashback.