This is an internal wall where the brown sediment (is it drywall? Plaster? Or something else entirely?) behind layers of paint is crumbling away causing holes.
You can see from the photos where the holes have formed but also cracks above where holes are likely to form. That part of the wall moves under slight pressure which makes me think the wall is crumbling there too.
What would be the best way to fix this up before redecorating?
The fix is simple enough although it may end up being a lot of work and or money.
The first step is to remove all the crumbling material and then determine the cause of this. A wall made of drywall should not be moving and so whatever is causing your movement needs to be corrected. What's going on here may be a symptom of a major structural problem so if that's the case you DO want to sort it out.
Once the root cause is corrected, you'll want to replace and re-finish the drywall using the normal methods.
It's hard to tell if this is a piece of drywall or it's plaster but it looks like drywall to me. It also looks as if there may be moisture involved in whatever process is causing this. So be on the lookout for leaks as well.
