Introduced birds are ones which were brought on purpose to the US, either for game hunting or because someone missed them from their native lands. The common pheasant is one example - this bird is native to central Asia, but now is found in much of the eastern US.
Two other well known introductions are the House Sparrow, from England, and the Common Starling, from Europe. The House Sparrow was brought in by many groups to help combat a few inchworms. They did eat them, but they also pushed out a number of native birds. The pests that those native birds ate multiplied and became much more of a problem than the inchworms had been.
Starlings were likewise thought to be good for combatting pests, but with their love of vegetables and grains, they have become a pest themselves for many farmers.
Other introduced birds include the mute swan and the rock dove.