There's relative poverty and absolute poverty, the latter of which is defined by the World Bank as people who live on less than $1.25 a day. There is a lot of literature on poverty, its causes, and their consequences. Many economists have indicated that large income disparities in countries have an adverse effect upon economic growth, and a huge distinction between developed (what some would say first world) and developing (third world) countries is that the latter has a higher rate of poverty and income disparity.
Poverty is often characterized by high mortality rates and severe deprivation of basic human needs, including food, safe drinking water, sanitation facilities, health, and education. Poverty reduction, in addition to being seen as a basic human right, is often associated with freedom and democracy.
I'd like to think the world can absolutely exist without absolute poverty, and with minimal relative poverty, and that it would be better for it.
To quote Muhammad Yunus in his acceptance speech for the 2006 Nobel Peace Prize: "To me poor people are like bonsai trees. When you plant the best seed of the tallest tree in a flower-pot, you get a replica of the tallest tree, only inches tall. There is nothing wrong with the seed you planted, only the soil-base that is too inadequate. Poor people are bonsai people. There is nothing wrong in their seeds. Simply, society never gave them the base to grow on. All it needs to get the poor people out of poverty for us to create an enabling environment for them. Once the poor can unleash their energy and creativity, poverty will disappear very quickly."