Thousands of pages are being written about how his portrayal brought the character back from the precipice of obscurity and put 'camp' into the ordinary person's vocabulary. I don't feel a need to add to those.
But a lot of discussion focuses on how different and unique(ly amusing) West's portrayal of Batman was. I want to focus on something he brought to the character that is NOT unique, but he brought it with such strength that it has informed every single portrayal of Batman since. Simply put:
(Adam West's) Batman did not care what you thought about him. At all.
Adam West didn't 'play' camp. He didn't wink at the audience or his fellow actors. He didn't wink at anything. Or blink, even. You want cute winks? Be a Superman fan.
Adam West took Batman with deadly earnest. Which is exactly how Batman takes Batman. A billionaire dressing like a bat to beat up muggers at night and throw boomerangs at deranged criminals is a RIDICULOUS concept. Intrinsically. The only thing that saves it from feeling ridiculous is the sincerity with which Batman does it. And nobody, I mean NOBODY, radiated sincerity more than Adam West.
It didn't matter what they made him do as Bruce Wayne; he was committed to its veracity 1000% percent. Dancing the Batusi was exactly as sincerely in character for West's Batman as recounting his parents' murder....BOTH of which happened in the first episode, in case you didn't know.
West's Batman (and most subsequent Batmen) don't care whether you think dressing like a bat is ridiculous. He doesn't care whether you cynically deride Virtue, the Constitution, Mercy, Caution, Civic Duty, Driving Safety, Dancing, Nature Studies, or Foreign Language study. HE understands and believes completely in these things and their value, and if you do not, he merely pities you (in a non-judgmental way, of course). He takes those things seriously.
Michael Keaton's and Diedrich Bader's interpretations of Batman were dead-on and well received. Why? Because those comedians understood the importance of Batman remaining serious...whether you want him to invoke fear OR laughter. Even LEGO Batman, the most overtly humorous screen interpretation of the character, has one central characteristic that is source of nearly all its humor: he takes himself very seriously, no matter how ridiculous his behavior or situation might be.
I have always felt that this is the essential conceptual conflict between Batman and the Joker; that Batman takes everything seriously and the Joker takes nothing seriously, without regard to the situations. That's why, objectively, Batman is hilarious and the Joker is terrifying. But that is perhaps another story for another time.
For now, I thank the late Mr. West for bringing sincerity to his role as Batman... and to everyone else's Batman, too.