It’s a good but not complete indicator. There is a very strong tendency for a country with a rising GDP to also feature people getting jobs, earning good wages, and increasing their disposable income. Likewise, a shrinking economy is often a sign that something is wrong. But this is a tendency, not a law of nature — if GDP rises because of a new oil discovery, for example, whether or not that brings broad-based gains or just a windfall to whoever owns the oil depends heavily on policy factors.
What’s more, GDP doesn’t measure lots of aspects of what makes a country a great place to live. A country can have major environmental problems like pollution despite (or because of) its fast-growing economy, for example. GDP also doesn’t tell you anything about crime rates, family structure, health, or happiness. A spike in the divorce rate, for example, might lead to a small surge in GDP as people need to furnish new apartments. But broadly speaking, economically strong countries tend to do well on health and other indicators.
In other words, you could say that healthy GDP growth is necessary but not sufficient for a nation’s long-term well-being.