Cobain and his friend Kathleen Hanna (lead singer of the feminist-punk band Bikini Kill) were sitting around Cobain's apartment, drinking beers to pass the time in the aftermath of a 1991 double-date that also featured Nirvana drummer Dave Grohl (who was seeing Hanna at the time) and Bikini Kill's Tobi Vail (who had been casually dating Cobain for several months, and with whom Cobain was hopelessly in love). At some point, Hanna busted out a can of spraypaint and began scrawling cryptic messages on the apartment's bare walls. Above Cobain's bed, she wrote, "Kurt smells like Teen Spirit."
Cobain took it as a compliment, thinking Hanna meant to say that he still carried the spirit of teenage rebellion.
If only Kurt Cobain had known that Teen Spirit was, in fact, a brand of deodorant, he might have realized that Hanna was gently (or not so gently) mocking him for being so smitten with her bandmate Tobi Vail. Vail, you see, wore Teen Spirit; Hanna's graffiti suggested that Tobi had marked Kurt with her scent.
Maybe she meant it literally, as in: Cobain still had the smell of sex on him following his last encounter with Vail. Or maybe she meant it more metaphorically, as in: Vail had Cobain whipped, so much so that he made it seem like she was around even when she was gone.
Either way, Kathleen Hanna was using a can of spraypaint to make fun of the fact that Tobi Vail had become the most important thing in Kurt Cobain's life in the summer of 1991. Cobain's subsequent rejection by Vail—she told him she no longer wanted to be with him after just a few months of casual dating—provided the emotional fuel that drove Cobain's songwriting on many of the best-known songs on Nevermind… "Smells Like Teen Spirit" foremost among them.
It's hard not to hear the song's closing lines—Cobain's raspy voice screaming "a denial, a denial, a denial…" over and over again—without thinking of Tobi Vail. Cobain's problem, the emotional crisis that propelled his music to such heights, was—ironically—that Tobi Vail was gone, meaning that Kurt Cobain didn't really smell like Teen Spirit anymore.