you have more wealth in real terms.

Basically, that means that your purchasing power is greater. As a country, if the average citizen's purchasing power is greater than the average purchasing power of another country's citizens, you can consider the first country more wealthy. And by "wealth in real terms" and "purchasing power" I mean your ability to purchase and use more goods.

As an example, the people of India, on average, cannot buy much. For many people, basic necessities of Western Civilization like toilets are too expensive. In America however, the average purchasing power of a citizen is much higher. It is rare to find someone who cannot afford basic plumbing, for example. As such, we can say that America is "wealthier" than India.

Also, you have to remember that GDP isn't the best way to measure economic growth, mainly because it only measures consumption in a limited sense. GDP measures consumption of all consumer goods and some capital goods. A better method would be one that measures consumption of all consumer goods and capital goods. That way, we could also see how the economy grows when people begin to save and invest more and consumer less.