Disclaimer: I believe that hedge funds in general are a net good for the economy. They take the other side of many trades that allow pensions and institutions to manage risk. As a whole, they are not all evil.
The current situation in Argentina is a remnant of an economic crisis in the early 2000's. During this time, Argentina suffered a large recession, and so was unable to make payments on US dollar denominated sovereign debt . Over the next few years, Argentina negotiated with ~93% of its creditors to make smaller payments of a lesser value instead of just not pay. These deals are common. Some of the bond holders had sold their bonds to a series of hedge funds, who would take legal action to force Argentina to pay the full amount.
Because the bonds were issued in New York, they were technically governed by US Securities Law. The securities law in particular that affects this situation forces Argentina to pay every bond holder the same. Argentina attempted to ignore the holdouts and make its payments to the 93% of bondholders who had agreed to lower payments, only to be blocked by hedge funds who held the other 7%. The hedge fund blocked them using US courts.
Argentina has refused to pay the holdouts the full amount, because it would then be forced to pay all of the bond holders the full amount. This sum is around 400 billion. They can't print money to pay the bonds, because they would print pesos and have to buy dollars to repay the bonds, destroying the value of their own currency.
A sovereign country should not be ruled by foreign courts. Argentina is not a US colony. Using legal methods to wrangle money out of broke emerging economies is despicable. Especially when those countries are attempting to make payments as agreed with their creditors. The investors who actually purchased the bonds with the intent of actual investment have agreed to restructure, leaving only vultures to extort Argentina.