That's one big hole in the wall. Don't be too shocked; nowadays, walls are kind of like slightly enhanced egg shells. They don't break in a touch, but they do crack a lot.
So sometimes, when construction workers tear down walls to join two rooms into one cutting the wall out is pretty easy. It's the wood/steel in between them.
However I've never seen a hole in the wall of that size that was made by a human fist.
Especially on the wall inside a house.
I punched my wall and nothing happened. It was a strong punch but my fist felt like it was on fire. I remember a friend (Who also plays basketball and is on my school's basketball team) got pissed himself and punched his wall. He suffered like me. And no hole, not even a crack.
So I would say that that wall is either weak, poorly manufactured, or old.
What to do? I would suggest trying to get that wall repaired and strengthened.
But, we all have financial issues so you may want to try something else.
Do you have a bookshelf or an everyday object that you put against a wall? Move it there. Got a poster you just bought and can't find a place in the room? There's a free spot right there. Maybe you want a little window allowing you to look at the wood behind your wall? Stick some transparent material onto it.
There you go. Problem solved, and case closed.
Hope my post isn't too long.