How did the Four Olds relate to the goals of the Communist Party?

During the Chinese Cultural Revolution (1966-1976), the Communist party sought to attack and destroy the Four Olds of Chinese culture. These were Old Customs, Old Habits, Old Ideas, and Old Culture. The failure of Mao's Great Leap Forward had damaged his standing in the Communist party as well as the public's opinion of him, so he gave societal reform one more try with the Cultural Revolution. By destroying the Four Olds, Mao and his Red Guard sought to make Chinese culture, art, literature, and education more in line with his ideal of a true Communist society. The Four Olds were never explicitly defined, but anything that seemed to be a threat to proletarian society and ideology was destroyed.

A number of historical buildings, including religious sites and temples, were destroyed; other places were given new, proletarian names. Libraries were destroyed and their books burned. Mao's Red Guard were specially tasked with destroying any bourgeois elements of culture and acting as enforcers in their own schools and towns. 

The Four Olds were really a target for cutting out anything that didn't fit into Mao's ideal of a highly controlled Communist society.