GDP measures the total production of an economy; in other words, the total value of all the goods and services a country produces. But it does not measure how that production gets distributed as income and benefits to the people living in that country, nor does it measure how those goods and services affect standard of living. Traditionally, GDP also does not measure the negative effects of production: environmental pollution and disruption, worker injuries and health, resource depletion, etc.
In general, as we look around the world, GDP per capita strongly correlates with quality of life indices. Countries with higher GPD per capita tend to have higher standards of living. More goods and services tends to result in higher standards of living.
But, two countries with similarly high GDPs per capita may differ significantly in wealth inequality and public services: one country may have higher taxes on its very wealthy citizens which in turn fund social programs that reduce poverty and improve public health and education, resulting in a more equal quality of life across its population. The other country may have lower taxes on its wealthy citizens, and in turn it spends less on programs that address poverty and public health, resulting in greater inequality and a lower quality of life for most citizens. Another classic example is pollution from economic production: a country or state that has a lot of oil refineries may be able to achieve a higher GDP at the expense of greater air pollution and reduced quality of life.
A good way to think of this relationship is: GDP measures the total size of the pie, but not how the pie is divided up. Standard of living measures quality of life, which usually means measuring access to healthcare, education, employment opportunities, cleanliness of the environment, ability to pursue personal goals, crime level, and treatment of people who cannot work such as the elderly or people with disabilities.