Hey there, I will make a few comments which will perhaps shed some light on the matter. Some other posters above went into a lot of detail about how the Fed works and is organized, but I will lay a foundation for your understanding. I have a degree in finance and I have worked at an investment bank, as well as several other finance related roles.

First, one thing we all have to understand is that our economic system is entirely based on CONFIDENCE. Unsophisticated people usually stop their understanding here, and sometimes adopt a defeatist, usually conspiratorial, worldview. But lets think deeper than that.

How is the entire economic system based on confidence, you ask? It is because we all kind of agree with each other to fulfill claims at some point in the future. Open your wallet and take a dollar out. That dollar is really just a claim to some future resource, such as a cheeseburger, a hair cut, or some pieces of gold. A dollar is only worth something because it is a medium of exchange (currency) - we all agree that it is worth something and at some point will be able to be put to use.

Now most people get this concept, but stop there. They really don't understand how the banking system works. I am going to assume you know what fractional reserve banking is (remember that scene from A Wonderful Life?). Now, since as we said earlier, everything is based on confidence, what happens when people -LOSE- confidence? This happened in the 1920's and caused the great depression. So we needed someway to restore confidence in the financial economic system so that people wouldn't run on the banks.

So we created the Federal Reserve (the Fed). It is a central bank that ALL other (major) banks have accounts with, and keep THEIR money with. Citi, JP Morgan, BofA, etc. all have bank accounts with the Federal Reserve and they keep their RESERVES in this account (keyword. remember fractional RESERVE banking?).

The Fed is unlike any other authority on the planet. I could go deeply into its structure, but just agree with me that it is highly independent and is made up of largely PRIVATE individuals (bankers, economists, etc.). We as Americans decided to do this many many years ago because we realized that politicians make awful economic policy decisions. Almost none of them are economists or businessmen, and they have very little idea of how the world works outside of D.C... So that brings us kind of to the first point that always makes me laugh with these videos. The Federal Reserve is NOT controlled by the Government. The Fed is far far more powerful than our politicians, actually. And this is a good thing. Because if we had this kind of power in the hands of politicians, they would be toying with the economy to win the next election by manipulating the CONFIDENCE in the system to make themselves look good by the end of a cycle. In doing so, they would make poor long term decisions in favor of good short-term decisions.... Also, it is worth noting that the Fed is dispersed across the country in 12 different cities, each with semi-equal representation, so that the economic interests of different regions of the US are represented.

So that is kind of WHY the Fed exists. Now I will talk a little bit about how they go about providing this "CONFIDENCE" we spoke about earlier. The Fed does have the power to make money. This is not insidious, it is necessary for a financial economic system to have merit. Why? Because it has two goals: (1) Control inflation and (2) keep unemployment as low as possible. In a nutshell, inflation and unemployment are largely symptoms of a lack of confidence in the financial economic system. So the Fed can restore that confidence by tinkering with the money supply. Obviously it won't just keep arbitrarily making money because that would make money worthless (inflation).

So it controls the money supply which in turn controls interest rates (because more money means money is cheaper to get, so interest rates will be lower.... LESS money means it is MORE expensive to get, so interest rates will be HIGHER). As Interest rates RISE.... economic activity will slow because it is more costly to finance things... as interest rates FALL... economic activity will heat up because hey, I think I will take out that $10,000,000 loan to build that car shop I wanted to. So the Fed has to find the right amount of money to pump or remove from the economy that will keep interest rates low enough to promote economic activity, but not too low because that would mean they put TOO MUCH cash into the economy and inflation would run rampant. They need to "take the punch bowl away from the party just as it gets started" - they want to give the economy just enough CONFIDENCE that everything will be okay.

This is where some people freak out because they think that the Fed is just creating money out of thin air for whatever insidious reason. The real reason the Fed is currently pumping money into the economy (by basically just dumping cash into the RESERVE accounts of those big banks we talked about earlier) is because they want to keep interest rates VERY low... they are at some of the lowest levels in history and have been since 2008 because the world economy has dramatically changed since then. In other words, the economy needs a ridiculous amount of cash to keep it going because we lost so much confidence in 2008 because financial institutions acted recklessly with everyone's money, as well as other macro-economic factors that will never reverse (i.e. a lot of US jobs going overseas, technology taking away people's jobs, etc.)

I just kind of puked information here and I didn't explain things fully. But this should guide your understanding and you should be able to Google further questions. Or feel free post them here and I (or hopefully others as well) will try to answer them, because I do not know where exactly you are in understanding this. I have also been awake for like 20 hours.