"Venus In Furs" is inspired by the novella of the same title, written and published by Austrian author Leopold von Sacher-Masoch in 1870. It tells the story of a man who wishes to be dominated and treated as a slave by the woman he loves. We get the word "masochism" from Sacher-Masoch's last name, and the entire practice of dominance and submission from this and the works of Marquis de Sade, a male author who wrote from the opposite position of dominating women and treating them as slaves.
Today's modern lifestyle knows this song's subject as "BDSM." That's a combined acronym: "B&D" for "Bondage and Discipline," "D&S" for "Dominance and Submission," and "S&M" for "Sadism and Masochism." That last part was originally written "sado-masochism," and in the 1960s was regarded as a mental illness and a deviant behavior, to be treated with electro-shock therapy and abhorred by society.
Even today in the United States, similar to the outdated laws against homosexuality, there are various state laws against practicing any BDSM-associated activity. That is, even using a whip or handcuffs to play with your spouse (even with their full consent!) can land you in jail, or in other states merely selling such paraphernalia (such as a frat paddle or nipple clips) is a heavy offense. This stems from the original association with prostitution - it was thought at the time that no one would be willing to participate in gratifying such "perverted" desires without being paid for it. For this reason, it became yet another consenting-adult, victimless-crime prosecuted by law and thus subsequently embraced by the counter-culture, which explains why it was a popular theme for both underground arthouses and underground bands.
So, with this song and the band's name, was Lou Reed kinky? Probably not, since, as given in The Velvet Underground: An Illustrated History of a Walk on the Wild Side
, he called the band's namesake book The Velvet Underground
"the funniest dirty book he'd ever read." However, it was the association of kink with the sexual revolution and the counter-culture lifestyle that made it an indispensable part of shocking the sensibilities of 1960s audiences.