It is a measure of the economic activity (production of goods and services) within a country. It isn't necessarily very precise if a country has a large black market or barter trade. It can be used to gauge the size of an economy and is somewhat indicative of how productive and the potential income levels of the citizens.

Method of calculation is complex - broadly it can be calculated by adding the income of all the participants or alternatively by measuring the expenditure of all the participants - netting out exports and imports.

Is it important - yes as a broad macroeconomic indicator. It is a simple measuring stick but any deep analysis of an economy requires much better economic data (GDP is too broad and simple). But it isn't super important otherwise and certainly not much importance for everyday people doing everyday things.

For most of human history, we kind of thought that how rich a country was depended on how much money it has. That kinda makes sense, rich people have the most money so rich countries must have the most money. However, our thinking about this began to change in the 1700s.

Countries like Spain began bringing in enormous amounts of silver from the New World. Back then, most currency was made of silver (and other precious metals), so they had by far the most money. Despite all of this, Spain continually lost power and influence to two upstart countries: the Netherlands and England. These countries did not have access to precious metal on anything like the same scale as Spain, but were able to support larger navies, feed their population, and develop advanced technologies. People began to question the old notion of what makes a nation wealthy.

A Scotsman named Adam Smith wrote a book entitled 'The Wealth of Nations' and among many groundbreaking ideas, he argued that wealth goes beyond money and is actually all of the output of an economy (everything produced domestically), minus the inputs (things imported from abroad). When you turn wheat into bread, the wheat has become more valuable and you have become more wealthy, and on and on for everything in the economy. This is what GDP seeks to measure, all of the value created by production in the economy.

GDP just one measure, but it is very highly correlated with things that matter. Countries with higher GDP per person tend to have better schools and universities, lower infant mortality, longer lifespans, and higher overall happiness. Lots of other factors like inequality, political instability, etc. can play into it, but GDP is almost always the best starting point for any economic analysis.

To expand a little on what others have said:

It's a measure of the "official" economic activity in the country. As phiwong said, it doesn't do a very good job of representing illegal/black activity; in addition, it doesn't measure lots of human activity that has economic value but isn't transactional in a way that governments can track.

Childcare is a common example. The work of your kid's daycare counts towards GDP - it's one of the "services" in "goods and services." But when you pick your kid up and take them home, the childcare you perform is not counted. Childcare has measurable economic value, since people are willing to pay for it. But not all of that value is calculated as part of GDP. Only the part that involves one person paying another is. (And even then, it's only counted if the payment is reported to the government somehow - when you pay your friend's daughter to babysit, that probably isn't going into the GDP numbers either)

Is it important? By itself it can be kinda useful as a means to compare two countries. Having a higher GDP is generally desirable. It's also important to look at GDP per capita - the total GDP split among all the people in a country. This gives you a better sense of wealth. If you just look at GDP, Luxembourg ranks #72 - a couple of spots below Guatemala. This might lead you to believe that Guatemala is wealthier than Luxembourg. It isn't. Guatemala's GDP is higher, but there are a lot more Guatemalans than Luxembourgers, so that GDP gets spread a lot thinner. Luxembourg ranks #1 in GDP per capita and is considered extremely wealthy; Guatemala ranks #109 and is considered one of the poorer countries in the Western Hemisphere.

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