The act of Blowing Stuff Up is to cause something to explode, similar to BOOM! It is a highly popularized method of attack, seen mostly in movies directed by Michael Bay. It has also been seen in multiple shames.
In Real Life
In real life, blowing stuff up is a violent and unsafe practice. It is often done in war, especially when bombs are involved. After all, since bombs are explosive, they often cause stuff to blow up. People first started blowing stuff up during the Hyrulian Civil War, when Morshu first invented bombs. Aside from being used by Morshu himself, they were also purchased by the handful by Link, making the two of them the very first people to blow stuff up.
In Shames and Movies
In movies and shames, blowing stuff up is exciting, fun, and just all-around awesome. Many movies, especially the ones directed by Michael Bay, involve explosions and use them as an adrenaline-booster during a fight scene or tragedy. Shames use a similar tactic, employing explosions to make something more exciting. Examples of shame characters that blow stuff up are Morshu (as mentioned earlier), Link (as mentioned earlier), Squadala Man (occasionally, using the Squadala Bomb), and everyone in the Contra Force.