When you buy a bond, you are making a loan to the issuer. That bond is money owed to the buyer, making it an asset.
When the Federal Reserve buys a US Treasury bill, note, or bond, it is making a loan to the federal government because the federal government has appropriated more spending than it has received in revenues.
The Fed doesn't purchase from the Treasury. The Fed buys Treasuries from dealer banks.
This is called "monetizing the debt". Putting more money into circulation.
Because of the crash resulting from the global derivatives bubble, the Federal Reserve has also been buying Mortgage Backed Securities (MBS). This is also printing money and putting it into circulation.
The "money" that the Fed uses to purchase Treasuries or MBS' isn't "put into circulation." That money sits on the bank's accounts at the Fed and only circulates among banks. The net financial assets of the private sector have not changed. The Fed has exchanged one financial asset (a T-bill, bond, or MBS) for another financial asset (bank reserves).
What this does do is change change the capital structure and maturity profile of bank balance sheets. It would become inflationary if banks increased their lending.
A key component of inflation that is almost always overlooked is something called "the velocity of money".
If the Fed gave you a trillion dollars, and you buried it in your backyard, then that trillion dollars will have absolutely no effect on the value of the money in circulation. The velocity of that trillion dollars is zero.
Just so since the crash of 2008. The velocity of money slowed considerably. Which is precisely why the Fed has been printing so much more of it. The Fed is attempting to get more cash out there to increase the sluggish movement of money.
Put more money into more hands and some of it is going to move around.
The traditional measures of velocity of money are outdated in that they are too narrow. When we talk about "money" now we must consider things like collateral and collateral chains.