The term "global economy" is used to refer to the idea that the economies of almost all the countries in the world are dependent on one another to some extent. In other words, instead of having separate economies for each country or region, we have one economy for the whole world because so many countries trade with one another. This one economy is referred to as the global economy.
The global economy has impacted the US in a number of ways. The best-known impact of the global economy has been on manufacturing in the US. The US has lost huge numbers of manufacturing jobs because these jobs can be done much more cheaply in other countries where workers do not get paid as much as American workers do. On the more positive side, the global economy helps US consumers by allowing us to get the things we want for less money (because they can be made more cheaply in other countries).