I have read that the GDP of the world is growing. I do not understand how this is possible. If I make profits out of a commodity or a service, somebody pays me for it. Hence, their wealth has to drop. So, shouldn't wealth only get redistributed? If so, how is it possible for the world GDP to grow?
GDP is not a measure of wealth. It's just how many times money was passed along to someone else.
Imagine that you and your friend find an empty island and each of you has 10 dollars in their pocket (so, \$20 in total). You stay in this island for one year, but you eat the fruits that the trees give you. What is the GDP at the end of the year? \$0. Why? Because you didn't pass the money to anyone.
Now, let's say that for the second year, you decide to become a lumberjack and cut wood to make fire. Your friend decides to buy this wood from you for \$8. So, this is exactly what you said, your friend's wealth went down in the same quantity that yours went up. What is the GDP in this case? \$8. Note that it's not \$20 (the total amount of money in the island), nor \$18 (the amount you have accumulated) but \$8 which is the money that he gave to you in a market transaction.
Now, let's say that he decides to take the wood and make it a chair. You like the chair, so you decide to buy it and pay him \$10. Now the GDP is \$18 (\$8 from the first transaction and \$10 from the new one).
Here's where it might get confusing (although not so much). He decides to make a new chair for himself and gives you \$8 in exchange for more wood. Now, the GDP is \$26 which is larger than the total amount of money in the entire island! Indeed, this happens in every country: the GDP is larger than the money in the country.
Without printing more money, you can basically keep money changing from one hand to the other infinitely. A growing GDP only means that the money is changing from one hand to the other faster. Not that people have more money in their pockets.
There's no such thing as a law of conservation of wealth. Wealth is created and destroyed in many ways. It is created when society produces goods and saves them. It is destroyed in disasters, or consumed when we use up our savings.It is created when we create knowledge, software, etc.
In a toy example: when a society starts out without any saved food, it produces food, eats half and saves half, then it is richer at the end. The accumulated food is an asset.
There's all kinds of wealth in a society: patents, ideas, buildings, roads, cars, computers, education, etc.
What does not get created or destroyed are nominal claims that we have against each other: if I give you a paper promising to pay you 10, that makes you 10 richer and it makes me 10 poorer but that's it. This means that its pretty had to figure out what is a society's total wealth, because there's all kinds of claims, explicit or implicit that are hard to value.