Lets start at the Beginning.
Definition: Hyperinflation is inflation that is out of control. You'll see "inflation exceeding 50% a month" all over the web, but I can't find a good source for that.
My definition: Hyperinflation is inflation out of control to such a degree that extraordinary measures are necessary to cope with it, and extraordinary measures are necessary to end it.
Causes: Hyperinflation occurs when the government issues too much currency that is not backed by something of significant value. It's generally when the government prints money to pay it's bills.
In practical terms, the US Government doesn't "print" money to pay its' bills. It just makes it magically appear by selling Treasury securities to the Federal Reserve ("The Fed" - the central bank of the US - look it up). Uncle Sam calls up The Fed and says "Hey, we need another billion." The Fed writes a check for a billion dollars, hands it to Uncle Sam, who hands the Fed a billion dollars worth of Treasury securities. Treasury securities are IOUs that the government promises to pay back plus interest at some future date. Uncle Sam now takes that check and uses it to pay for government stuff. That's how the extra money flows out into the economy.
Here's the wierd thing: That check that the Fed writes? There is no billion dollars in the checking account. There's nothing. It's just a piece of paper. Somehow in this recursive self-referential yin-yang feedback ritual ceremony of exchanging one piece of paper (the Fed check) for another (the Treasury security), money is magically created!
When The Government and the Fed do this, we get inflation. When they do this too much we get hyperinflation.
Now, why would our beloved and trusted government do such a thing and how do they get away with it? Simple: To pay the bills. More bills + less income = create more money = inflation.
There are other factors that can cause inflation, such as rising oil prices which push up the price of everything else. But those factors by themselves cannot create hyperinflation. To really foul things up takes the power of government.