I don't think it is meant like "at some point you'll run out of things to buy", because, let's be honest, even the richest people still have things they can't buy. The actual meaning is in my opinion that at some point, when you can pay your bills easily and do not need to worry about money every day, increasing your income doesn't make you happier.

Of course, buying more expensive things and increasing your income is still a good feeling, but after some time they become status quo and your happiness is back at the same level as it was before the pay raise (especially since there are now new, more expensive things to seek).