Absolute poverty means that a family or an individual lack(s) all of the means necessary to meet the basic needs of life. When someone doesn't have a sufficient income to obtain food, shelter and water, they live in absolute poverty. Measuring absolute poverty can be used as a way to determine the degree of poverty in a certain country.
Relative poverty, on the other hand, is when a family or an individual is poor in comparison to other families and individuals. A person has a sufficient income to meet the basic needs, but not enough to obtain anything more than that. Unlike absolute poverty, relative poverty often depends on the country's economic climate, or rather the country's economic growth and development.
In the case of Jennie, for example, one might argue that she's living in relative poverty, as she can meet the basic needs of living: she has access to food, water, and shelter and can take care of her children, no matter how sufficient or insufficient that care is. However, due to the fact that she's been living in temporary accommodation for over a decade, some might argue that she might be actually living in absolute poverty, as her situation clearly remained unchanged, regardless of the country's economic growth or lack of growth.
It is notable to mention, however, that one may be living in relative poverty "permanently," meaning that the subject, who is relatively poor, may never enjoy the same comfort or live the same life as other people in the country. Thus, Jennie might be "stuck" in permanent relative poverty.
In this context, one disadvantage of relative poverty is that it doesn't show how many years someone spends living in poverty (Jennie, for instance, has presumably spent 12 years living in poverty). However, it does show what poverty might be like in a specific society at a specific time, as it can be used to measure the differences in income distribution.
A big disadvantage to both absolute and relative poverty is that the definition of poverty changes over time and is different in every country. For example, Jennie and her family may be considered relatively poor in the UK, but in another country that's economically more advanced, she might be considered absolutely poor.