The term "headset" refers to the set of bearings and cups that allow the fork's steerer tube to turn freely in the head tube. While sometimes the headset is overlooked, a quality mountain bike headset can make a major difference in how a mountain bike handles and turns.
Often, though, newer or inexperienced riders can't tell the difference between a cheap headset and a high-quality headset. But one thing is certain: the best headsets last a very long time and provide quality performance year after year, while cheap headsets will wear out rather quickly.