What is Economic Growth?
I sometimes talk about changes in the rate of "economic growth" (example). Here's a brief attempt to explain what this means. You can find much more complete explanations in economics textbooks (or at Khan Academy).
My best shot at an easy/short version:
 If you imagine a big farm with multiple farming families on it, exclusively producing crops, then GDP is the amount of crops they produce each year, and economic growth is how much GDP (their total crop production) goes up from year to year. Total crop production could go up because they're getting more productive (more crops per person), or just more numerous (more people growing crops), or some combination.
 In a real economy, there are all kinds of other things produced in addition to crops  including services, such as haircuts  but we convert them all to the same units (using their prices) to see how much total "stuff" is produced each year. Again, economic growth reflects some combination of more people and more "stuff" produced per person.
A bit more detail
 Every quarter or so, there are official estimates made of the total dollar value of all of the goods and services that are produced in a year (GDP).
 So in theory, if you buy a candy bar for $1 and get a haircut for $20, $21 gets added to GDP.
 In theory, "GDP can be measured either by the sum of what is purchased in the economy ... or by [the sum of all] income earned on what is produced." That's because everyone's purchase is someone else's income.
 There are also estimates made of the average change in prices for all the goods and services (inflation).^{1}
 "Economic growth" usually refers to how much GDP grows in a year, adjusted for how much prices rise in a year. In my view, the easiest way to think of this is as the change in how much "total stuff" (including services, e.g. haircuts) was produced in one year vs. the year before.
Misconceptions and imperfections in the concept
Economic growth doesn't necessarily measure people getting richer (having more stuff per person). Economic growth can be caused just by population growth. There is a separate concept, "percapita economic growth," referring to the amount of total stuff there is per person, which can be thought of as a measure of people getting richer or poorer.
Economic growth is subject to imperfect measurement. In particular, as estimated today, it only includes the value of transactions  things that people spend money on. So:
 If someone creates free entertainment and gives it to everyone (without selling advertising or anything else), this won't show up at all in economic growth figures.
 Things that family members do for each other (if not paid for) are not going to show up in economic growth estimates.
I don't think of economic growth as a perfect measure of what it's supposed to be measuring. But I think that major changes in it from year to year are usually meaningful.
 If economic growth has generally been around 2% per year, but this year it was 1%, there was probably some kind of negative shock to the economy (in fact, the most common definition of a recession is a certain duration of negative economic growth).
 If economic growth went from 0.1% per year in one period to 1% per year in another period, this probably indicates that the second period was a period of more rapid growth in the total size of the world economy. This was probably driven by some combination of more rapid population growth and more rapid "world getting richer."
 If economic growth is 0% or negative, and the population is stable or growing, this is probably a "zerosum" situation: the only way for one person's income to go up is for another person's to go down. This would be a different dynamic from the one we're all used to, in which it's not crazy to hope that the vast majority of people will have better material situations than their parents'.
 If world economic growth reached something like 100% per year, this would imply that the "total amount of stuff produced in the world" was doubling every year. This would be very different from today's world, where the world economy takes several decades to double. To get a very rough idea of what this kind of growth would be like, you could imagine that the world would change and expand as much each year as it currently does every few decades. This would be an unprecedented situation, and a lot of things would probably work very differently.
Simplified example calculation of economic growth
Let's say we are evaluating the growth in a tiny island economy:
 Say there are a total of 10 people. 5 of them ("rice producers") grow and prepare rice, and 5 of them ("beans producers") grow and prepare beans, and each meal is a mix of rice and beans, and that's all the economic activity. Despite this, people use money for some reason.
 Say that in a particular year (the year 2000):
 The 5 rice producers produce about 10,000 servings of rice (enough for 10 people for a year). They sell half of it to the beans producers, who pay $10 for each serving of rice. They eat the rest themselves. So that's a total of 10,000 servings of rice, at $10 each, or $100,000. (We are counting the value of rice eaten by rice producers, even though there was no official sale; in practice it's possible for GDP measurements to miss this sort of thing.)
 The 5 beans producers produce about 10,000 servings of beans (enough for 10 people for a year). They sell half of it to the rice producers, who pay $10 for each serving of beans. They eat the rest themselves. So that's a total of 10,000 servings of beans, at $10 each, or $100,000.
 The island's GDP is therefore $200,000: $100,000 worth of rice plus $100,000 worth of beans.
 Now say that in the following year (2001), we add two people: one rice producer, and one beans producer. So now there are 12 people, and more total meals needed. Also, for some reason the people on the island decide to print a large number of additional dollars, and the price of everything in dollars goes up.^{2}
 The 6 rice producers produce about 12,000 servings of rice (enough for 12 people for a year). They sell half of it to the beans producers, who pay $15 for each serving of rice. They eat the rest themselves. So that's a total of 12,000 servings of rice, at $15 each, or $180,000.
 The 6 beans producers produce about 12,000 servings of beans (enough for 12 people for a year). They sell half of it to the rice producers, who pay $15 for each serving of beans. They eat the rest themselves. So that's a total of 12,000 servings of beans, at $15 each, or $180,000.
 The island's GDP is therefore $360,000 ($180,000 worth of rice and $180,000 worth of beans).
 The island's GDP growth is 1.8x (technically, confusingly, called "80% growth"),^{3} because $360,000 (this year's GDP) is 1.8 * $200,000 (last year's GDP).
 However, a lot of the growth in GDP just comes from everything getting more expensive. Since everything is 1.5x as expensive ($15 per serving instead of $10), we can say inflation is 1.5x, or "50% inflation". (If some things changed in price more than others, putting a number on inflation would be more complicated.)
 As stated above, to get the island's economic growth, we need to adjust GDP growth for inflation. 1.8x ("80%") GDP growth, divided by 1.5x ("50%") inflation, corresponds to 1.2x ("20%") economic growth.^{4}
 A simpler way to think about this is that there are 20% more people this year compared to last year (12 people vs. 10), and so there is 20% more food produced and consumed compared to last year (12,000 servings each of rice and beans, vs. 10,000 each last year). Since food makes up the whole economy, this means the economy grew 20%. This reasoning would be more complicated in an economy with lots of different goods and services growing at different rates, which is why the more complicated dollarbased calculation is used, but "total amount of stuff produced" is what it's trying to get at.
Footnotes

Although the most commonly cited measure of price levels is different from the measure of price levels used for real GDP growth calculations. The former is CPI, and the latter is the "GDP deflator." Inflation usually refers to the change in CPI, but conceptually could just as easily refer to the change in the GDP deflator. ↩

The reason I'm assuming this is that in modern economies, this is usually what's happening: the total amount of money is going up every year, so prices are rising every year. Why this is would be a topic for another time. ↩

When someone talks about "X% growth," what they mean is that something was multiplied by (1 + X%). So if you start with $100, "10% growth" means you now have (1 + 10%) = 1.1x as much, "100% growth" means you now have (1 + 100%) = 2x as much, "300% growth" means you now have (1 + 300%) = 4x as much, and "20% growth" means you now have (1  20%) = .8x as much. I wish I could give you some good reason that people use this kind of terminology, but I think it is basically just a gratuitously confusing way of communicating, and it would be better if people talked about "1.03x" economic growth instead of "3%" economic growth. ↩

Why divide? One way of thinking about this:
 There is 1.8x as much GDP this year as last year. (This is the same thing as saying that GDP grew 80%.)
 But it costs 1.5x as many dollars to buy something this year compared to last year. (This corresponds to 50% inflation.)
 If you have 1.8 times as many dollars as you did before, but it takes 1.5 as many dollars to buy stuff compared to before, you can buy (1.8/1.5) as much stuff. For example, if you go from having $100 to having $180, but meals go from costing $100 to costing $150, then you go from being able to buy 1 meal ($100 / $100) to being able to buy 1.2 meals ($180 / $150). ↩