All I have read (admittedly not much) on the subject of the Cultural Revolution describes it as chaotic time initiated by Mao as a means of getting back on top, the only long-term impact of which is the new Chinese leadership's emphasis on stability. But it must have meant something in Communist terms, i.e. been presented a policy shift within Marxist-Leninist-Maoism with reasons and goals. What were they? Were any of them acheived? Did any of them last?
Deng Xiaoping and Liu Shaoqi saw the dangers of a dictatorship and attempted to set up internal checks and balances against Mao. They wanted Mao to only retain a symbolic and ceremonial figurehead, while the actual decision-making process will be left to the more experienced, more rational government officials. What they wanted to create is very similar to today's CCP: a faceless, authoritarian machine without any possibility of the emergence of an idiot dictator like Mao.
Keep in mind Mao was incredibly paranoid and was always very insecure about his power, in his mind he created a new elite from his previous revolutions of over throwing old elites. And this time around the new ruling class had deeply infiltrated into the Communist party and they were threatening the party's future.
Thus, as part of his revisions on Soviet Communism, Mao came up with the notion of 'Perpetual Revolution' in order to always keep his subordinates in check.
That's when the Cultural Revolution happened, young Chinese (Red Guards) with no authority or experience were given full permission to shame, torture and kill communist leaders on a national scale. Imagine completely uprooting the social order of a society by replacing experienced, rational government officials and scholars with young, inexperienced, and adrenaline charged young people.
This is a question best directed at Marxist-Leninist-Maoists, I think, try /r/communism101. /r/AskHistorians simply isn't equipped to deal with a question like this.
edit: I'm not sure why I've been downvoted for saying this. The OP asks for a Marxist-Leninist-Maoist perspective on the reasoning and goals of The Cultural Revolution, which means we're going into not just history - but Marxist economic theory, political theory and philosophy. /r/AskHistorians simply isn't able to handle this, and if it tries it's probably not going to be from a MLM perspective, but rather from a liberal perspective.
It hasn't been noted yet, and I see it as necessary to note, was that the Cultural Revolution was created to bring Mao back power he has lost due to the failure of The Great Leap Forward. It should be noted that by 1963 the country was being run by Liu Shaoqi, Zhou Enlai, and Deng Xiaoping. Mao was a symbolic figure (now only in charge of the Communist party as Shaoqi had become the nation's president after Mao was forced to resign post GLF) and he wanted real government power back.
After Shaoqi was forced from office it simply remained vacant. Mao wanted power in his hands and his hands only.