The Dude, aka Jeff Lebowski is the hero of the fillm The Big Lebowski.
It is the simplest possible accurate description.
The better description requires us to delve more thoroughly into the story a bit. This particular Jeff Lebowski is NOT "The Big Lebowski" of the film - that particular film has as a plot point that there are TWO Jeff Lebowskis in Los Angeles, California and at the beginning of that story a couple of hired torpedoes attack the wrong one. A shady character is owed money - a lot of money, in fact - by the young trophy wife of the other Jeff Lebowski and the story takes place as a result of Jeff simply wanting to be compensated for a lost rug.
To say any more would be to spoil an absolutely wonderful film that was a commercial flop in its initial release but became a cult hit.
One of the biggest strengths of the film is its characters, and The Dude resonates with a lot of people as one of the strongest. In contrast to the Jeff Lebowski who the hit men attack at the beginning of the film, a rich and well known philanthropist The Dude is an unemployed Baby Boomer slacker with little more to his name than a few outfits, a bowling ball and a nice rug that really tied the room together. He's a happy-go-lucky fellow who hides marijuana-reddened eyes behind Wayfarer sunglasses (at a time when it was still illegal in California to smoke it), an umkempt beard and moustache combination with long hair and an outfit comprised of an old raglan T-shirt, a set of drawstring pyjama bottoms and a decidedly unstylish 70s cardigan. The overall effect is something between a homeless hippie and an aging Seattle grunge rocker.
His only real ambition in life is to succeed at bowling with his friends in a local league bowling tournament, and to that end will actually lie on a floor meditating on the game by literally listening to audio of previous games through the headphones of a Sony Walkman. He gets away with occasional missing or late rent payment (and we get the idea that he gets a break on that rent) because he's such an unbelievably likeable fellow that the universe appreciates his personality and accomodates it.
He's the sort of guy who only brings up the subject of his ruined rug with the other Jeff Lebowski not because he's seeking damages as such for his pains - just that he is minus a rug, The Big Lebowski has sufficient capital to afford a warehouse full of them, and there's a principle involved. And, he only wants a replacement for the rug, no more, no less. When the other Lebowski dismisses him angrily, he simply shrugs his shoulders and tells the underling who meets him that he was told to help himself to a replacement rug.
Everyone around him has an agenda of sorts and tries to use The Dude to their own ends, but The Dude Is who The Dude Is and he Abides nonetheless. The Coen Brothers, when they wrote the film, wanted a Raymond Chandler type narrative in which the plot was ultimately irrelevant. Because of the collision of Bridges and the Coens, they've come up with a character who beautifully expresses the Taoist principle of wu wei. The Tibetan Buddhist crowd around the Shambhala foundation have decided that the character of The Dude is actually a bona fide Ascended Master, and as a Buddhist, Bridges kind of digs that.
And that makes The Dude's responses to things - his insistence when being muscled into the back of a car by two thugs towards an unknown and possible dark fate is to angrily insist that the two not spill his everpresent White Russian, his nonchalance at being asked point blank if he wants fellatio by a young and beautiful woman, and his complete indifference to the attempts by The Big Lebowski's staff to impress The Dude with his material and societal successes - obvious and par for the course.
It's inspired a lot of people. There's been a yearly-ish congregation called the Lebowskifest in which people dress as the Dude, go bowling, watch screenings of the film and just generally appreciate The Dude's way of life and looking at things.
In fact, there is even a religion that's ha ha only serious called Dudeism - anyone can self-ordain and do whatever - so long as they generally follow the action of no action and Zen out, man.
And the whole thing has clearly inspired Walt Disney who re-imagined Jeff Bridges' character in the Tron sequel as a kind of wandering monk figure - one who has achieved agelessness of a sort and lives in a minimalist corner of the computer world Tron takes place in. When we see the character again he's not the young brash fighter of the original Tron, but instead Jedi-like in dress and very Dude-like in overall vibe, even as the script calls for him to be a bit more worldly and involved than The Dude ever was.
Bridges, for his part, now gets a lot more props for being the kind of guy he is and hanging out in the kinds of clothes he hangs out in between films - after all, all the costumes in the film are Bridges' own clothes, and he does do a lot of Buddhist kind of things when he's on his own. In a way, Bridges kind of didn't really do much to land into the whole Dude thing - which makes the whole phenomenon Art Imitating Life. The script was written for him with him in mind to generally slouch around in his pyjamas as he is wont to do.
But as cool as Bridges is and as neat as the "Chinese Laundry" baseball shirt is he wears in many a film - he doesn't have Sam Eliott narrating his life story. Jeff Bridges is a man, but Jeff Lebowski is the Dude. And the Dude abides.