It matters fundamentally for two reasons. First: an estimated 5 trillion dollars worth of trade passes through it every year: whether that's plastic buckets coming out of Chinese factories or software computers or oil and gas.
"The fear is that if China successfully challenges one part of international law in one place, such as the South China Sea, then who's to stop China or any other country from starting to break laws all around the world?"
Secondly and more fundamentally, it's about rules and it’s about who sets them. There are rules such as the Law of the Sea, that various countries have agreed to. What China has tried to do, however, is to stretch and or possibly break those rules in order to fit its own interests in the sea. For example, China has the idea that it can claim the right to the fish and the oil more than 200 nautical miles away from its coast. If China were to do that, it would, in effect challenge the law of the sea.
https://www.youtube.com/embed/NYz8foAolj0?wmode=opaque
The fear is that if China successfully challenges one part of international law in one place, such as the South China Sea, then who's to stop China or any other country from starting to break laws all around the world? And then, what happens if nobody respects international law? We'd be back to the principle of Might is Right, where everybody's got to build up their armed forces to fend off everybody else. The U.S. wants to hold the line about the Law of the Sea and the way conflicts and disputes are resolved because if it doesn't do so here, then it fears the unraveling of the post-Second World War international order all around the world. That’s why it matters.