There are two standard models for measuring poverty in North American political circles.
The Low Income Cut Off (LICO) is a relative measure of poverty. Thus, if income rises for everyone, "poverty" stays the same. It is more of a measure of income equality than of poverty.
The Market Basket Measurement (MBM) gives an idea of how much a person can afford to purcahse in comparison to their income. It is an indication as to whether or not a person can afford what we deem to be the basic necessities of life.
It is also important to differentiate between Western poverty and 3rd woerld poverty.
Firstly, let me address Western poverty.
Western free market society is designed to provide opportunity, as opposed to guaranteed income. As such, most people are able to succeed in our society. However, for various reasons - some are not. It may be because of an addiction, a learning disability, emotional instability, lower intelligence, or a range of other less apparent reasons.
While we provide charity to many individuals, the prevalent fear of removing incentive to work, and/or giving aid to individuals that don't need it prevents us from covering everyone in need of help - and so, there are people in Western society in legitimate need of help who do not receive it.
The other main reason why poverty still exists in affluent societies is economists who announce that 'the sky is falling' each and every time that a policy is suggested that will help the poor at the expense of the wealthy. Each time, taxes are raised in such an endeavour, the nation is said to be less competitive - as if the only way that we can all avoid poverty - will be if we throw the least fortunate to the wolves.
As for international poverty, there are many causes. The biggest one, is not lack of natural resources as some might suspect. The biggest cause is lack of education which is usually a direct result of corrupt governments and interference by Western nations hoping to keep the people uneducated so that they can exploit their cheap labour and/or get their natural resources for next to nothing by cutting deals with the corrupt leader - who is able to pull a smokescreen over the relatively uneducated populace.
Relative poverty will always exist to some degree. Absolute poverty could be eradicated if the United Nations put some strict controls in place to ensure proper education for all peoples, and the control of their natural resources. "Fortunately", for the West, we have five nations with veto powers over the UN who will ensure that the poor nations of the world never climb out of their hole.