Wiktionary
n. (context politics English) A political party with a strong influence in a country's politics.
Wikipedia
A major party is a political party that holds substantial influence in a country's politics, standing in contrast to a minor party. It should not be confused with majority party.
According to the Merriam-Webster Dictionary:
Major parties hold a significant percentage of the vote in elections and claim higher membership than minor parties. Typically, major parties have the most donors, best-organized support networks and excellent funding for elections. Their candidates for political positions are closely watched since they have the highest chance of being elected to office because of the high membership, recognition and donations that these parties are able to generate.
Two major parties can lead to a two-party system. If there is only one major party, then it is a dominant-party system. In a multi-party system, a major party is one that occasionally controls the presidency or premiership and is the most influential party in a coalition government.
Usage examples of "major party".
Put my faith in one of the major party candidates who were being funded by the same big shots I spend my time fighting and filming?
This has never been proposed by a major party candidate for the Presidency and is not now proposed by Lyndon Johnson.
It is well understood in political circles diat public office or major party office is almost always badly underpaid for the talent and experience die jobs need.
It had a drunken and lopsided look, as though it was hung over after some major party.
The Saudi ambassador threw a major party last weekend for the congressional leadership.
Yet he was beloved in his state, and there were enough voters in the country dissatisfied with the direction of the major party platforms that Ritter had run for president, as an independent.
I rejoined that the Klan is a mere lunatic splinter group, not a major party capable of governing the nation.