Within academia, "cultural Marxism" is simply Marxian theory applied to cultural studies - the analysis of memes and institutions in terms of historical materialism.
As a political epithet, it originated in the title of a book: Kulturbolschewismus by Protestant theologian Kurt Hutten, published by the pro-Nazi Volksbundes in 1931. Hutten's argument was that Marxism threatens to bring about a cultural revolution, which all right-thinking people should oppose:
"Cultural-Bolshevism aims at the destruction of our existing culture and wants to reconstruct it so as to serve man’s earthly happiness."
He spells out a distinction between "earthly, material" pleasure and "faithful, idealistic" happiness:
"Cultural-Bolshevism is not a recent thing. It takes as its basis a striving that was planted in man’s constitution in primeval times: The intense longing for happiness. It is the primordial nostalgia for paradise on Earth. [...] The religion of faith is replaced by the religion of pleasure."
Like many Christian philosophers, Hutten believed that earthly pleasure is sinful and "true happiness" can only be achieved in religion. And like many Christians of the post-Darwin era, he saw the rise of a secular atheistic intelligentsia as dangerous - once "God is dead", people lose their God-given moral code and become materialistic hedonists. He was also a Nazi-supporting antisemite, and took Point 24 of Hitler's National Socialist Program (declaring a Nazi culture-war against "Jewish-materialism") to heart.
The evil of "cultural-Marxism" (also called "Jewish-materialism") is thus the antithesis of good "European religious morality". Hutten's view of which side of the culture-war he was on:
"Marriage as a tie, family as a duty, Fatherland as a value in itself, morality as authority, religion as an obligation deriving from eternity."
According to Nazi ideology, Marxism Judaism and capitalistic-materialism are all one and the same thing, because, um, y'know, reasons. Just like the Pope often talks about how immoral capitalistic greed is, the Nazis denounced the "materialism" of the "money-hoarding supercapitalist leeches", meaning unregulated merchant-capitalists (a class that is 110% Jewish, because trufax).
Marxism is an atheistic modern philosophy, and a political-economy movement with the ultimate goal of optimum material conditions for everyone. For idealists like Hutten and Goebbels, this is merely another philosophy of hedonistic materialism just as bad as liberal supercapitalism... and it happens to be named after a Rabbi's grandson. That's why Hutten singled out "the Bolshevik cultural revolution" as the principal threat facing western civilisation.
Ergo, "cultural Marxism" (in eyes of fascists and conservative Christians) is an evil social movement that seeks to bring about a Godless materialistic ethic in which people only care about acquiring more personal wealth through either usury (in the case of hook-nosed greedy capitalists) or undeservedly-high wages (in the case of deluded lazy socialists). It seeks to destroy religion, family values, nations and every kind of moral authority (yay!). When the term is thrown about as a slur, it's because they believe that their opponent is somehow working for the Marxist (Jewish-materialist) side in this great culture-war.