A vanguard party is a political party

Political party

A political party is a political organization that typically seeks to influence government policy, usually by nominating their own candidates and trying to seat them in political office. Parties participate in electoral campaigns, educational outreach or protest actions...

 at the forefront of a mass action, movement, or revolution. The idea of a vanguard party has its origins in the Communist Manifesto by Karl Marx

Karl Marx

Karl Heinrich Marx was a German philosopher, economist, sociologist, historian, journalist, and revolutionary socialist. His ideas played a significant role in the development of social science and the socialist political movement...

 and Friedrich Engels

Friedrich Engels

Friedrich Engels was a German industrialist, social scientist, author, political theorist, philosopher, and father of Marxist theory, alongside Karl Marx. In 1845 he published The Condition of the Working Class in England, based on personal observations and research...

. The concept is most well known for being put into practice by the Bolshevik Party in Russia.
In the Chapter II: Proletarians and Communists of the Communist Manifesto, Marx and Engels outline the role of a communist party as a proletarian vanguard party:

The Communists, therefore, are on the one hand practically, the most advanced and resolute section of the working-class parties of every country, that section which pushes forward all others; on the other hand, theoretically, they have over the great mass of the proletariat the advantage of clearly understanding the lines of march, the conditions, and the ultimate general results of the proletarian movement.

The immediate aim of the Communists is the same as that of all other proletarian parties: Formation of the proletariat into a class, overthrow of the bourgeois supremacy, conquest of political power by the proletariat.

As he surveyed the European milieu in the late 1890s, Lenin found several problems with the Marxism of his day.