The term "major pair" in the forex market generally refers to the most heavily traded US Dollar currency pairs. EUR/USD (Euro vs US Dollar), GBP/USD (British Pound vs US Dollar), USD/CHF (US Dollar vs Swiss Franc), and USD/JPY (US Dollar vs Japanese Yen) are almost universally regarded as major pairs.
AUD/USD (Australian Dollar vs US Dollar), USD/CAD (US Dollar vs Canadian Dollar), and NZD/USD (New Zealand Dollar vs US Dollar) are sometimes included but are less popularly traded than the big 4.
Originally, these pairs were referred to as majors because of the United States dominance in the world economy during the floating currency rate era (since the 1970s.) In many ways, you could say that these currency pairs are to the forex market what the blue chip shares are to the stock markets. They are the most popularly traded (highly liquid) instruments in the foreign exchange world.
Whether or not a pair is considered a major isn't much of an issue but it's worth knowing what most professionals are referring to when the term is used to distinguish them from cross pairs. The main distinction is that these "majors" are not cross pairs (crosses don't involve the US Dollar.)