One obvious answer is that it stops us from dismissing the poor in our own (rich) society with the claim that they’re not really poor. (“How can they be poor? There are really poor people in Africa, but these people have beer bellies and colour tellies.”) Then there’s the point that different societies work in ways that aren’t always easily commensurable in terms of income, property, and social relations. Five US dollars will get you a lot further in most poor countries than it will in the USA.
The flip side, however, is that relative measures tend to focus attention on redistributing wealth within countries, but at the cost of disguising the necessity of redistributing wealth between them. “Poverty” becomes a sign without a stable referent, denoting quite different states of affairs dependent on deictic legerdemain - a kind of global post-code lottery. Cui bono? The rich, of course, many of whom have pleated the word “poverty” into a decorous fan behind which they can say “A million pounds really isn’t much these days, you know” - and actually mean it.