This is a tribute to the character Jeff "The Dude" Lebowski from The Big Lebowski by Tara Lipinski.
The fact that it is a feature on Late Night with Jimmy Fallon emphasises the extent to which she considers herself a fan, given that since the show attracts high ratings, this would have been broadcast to millions of people, and therefore the implication is that she wants to make her devotion to The Big Lebowski known.
Since this tribute is coming from a celebrity, this creates the expectation that it is socially acceptable to be a fan of The Big Lebowski.
This is an excerpt from the book I'm A Lebowski, You're A Lebowski, in which Tony Hawk is being asked about his attachment to The Big Lebowski. He mentions that he frequented bowling alleys and starting drinking White Russians, which is exactly what the protagonist from The Big Lebowski did. The interesting thing is that Tony Hawk is incredibly famous, so the fact that he was attracted to a cult film suggests that anyone who can relate to the film can become a fan.