This is an article about Vulnerability and they mention a quote from a director that I don't understand:

"Apparently, the great director Ang Lee once reminded an actor, concerned about their performance ’Don’t worry. Audiences don’t come to see you, anyway. They come to see themselves.’ If he did indeed say that, he could not have put it more succinctly. We often suffer from the misguided belief that our supposedly perfect, untarnished self is what an audience wishes to see."

What does this quote mean? I don't get when they say that people want to see themselves or that they would rather see someone act in a flawed or poor way than in a perfect way. If this is the case, then why do actors like Nicolas Cage and Tommy Wisseau live in infamy for being bad actors? I mean, if people want to see actors be vulnerable/susceptible to criticism and not perform their part in a way that's convincing, then they should love it more than citizen cane.

Wow, you took a huge leap off on a tangent with 'susceptible to criticism.' Being a flawed character that we flawed viewers can relate to has nothing to do with poor acting subject to criticism.
I don't know what to say if you don't see that.... think about it and come back.

Could you link the article to give us some context? Really hard to measure one small snippet without a picture of the whole thing. I notice you like picking out parts to examine. I think understanding comes better with a better view of the entire picture.

Can you help me with that?

Link to full article

Vulnerability in Acting | Acting Tips

Link to full article

http://www.stagemilk.com/vulnerability-in-acting/

No, I understand why we’d want to see flawed characters played perfectly by actors. But here they’re saying that an actor’s performance of a flawed character is flawed or imperfect

I never said we'd want to see flawed characters played perfectly. The whole gist of this is that Ang Lee was saying don't try.

Well maybe perfectly was too strong a word. But I mean at least play it convincingly. If someone is nervous on stage and sucks at acting, people aren't going to like the character simply because they can relate to being scared or vulnerable. And I can't believe Ang Lee, a movie director, out of all people, is saying this... that is if the meaning is what I think it means.

You are taking what is drama way too seriously to see the context of what the opinion of a good actor is. That's Ang Lee's OPINION, and his alone. He is successful to some, but not to others. The same goes for actors as they are popular with some and not others. The article is about vulnerability, and the quote is just to illustrate a trait he wants HIS actors to bring to the production. Other's in this industry have different styles simply because they have a different audience, or a different perspective how to relate to the audience.

This article is the opinion of the writer and just uses a particular director to illustrate the point.

What does vulnerability even mean in the context of the article. I always thought it was being susceptible to criticism or being embarrassed. Which I guess is fine if the character is supposed to be shy/embarrassed but if not, why, in Ang Lee's opinion, would an actor being overly emotional when the part doesn't require that be considered a good thing?

Vulnerable in general means unprotected, able to be attacked.
Vulnerable in the the sense Lee means refers to a person who lets cracks open in his or her exterior to be affected emotionally by the person he is interacting with, or the scene. Not criticism from the viewers!
Hurt is usually the emotion I think of when I detect vulnerability. Hurt, sensitivity, old wounds, old fears, something unknown, a fallen baby bird quality.
It doesn't have to be dramatic or obvious. It can be just a look in the eyes, or a change in the voice, or a pause - all sorts of tiny ways.

You asked above why Nicolas Cage lives in infamy as being a bad actor? LOL, I happen to like his acting. I think he exudes vulnerability. Moonstruck might not be great art, but it's a wonderful movie, with Cher telling Cage to 'snap out of it' when he professes his love.
Sure, the really best actors restrain their vulnerability, as most of us do throughout our humdrum lives, to protect ourselves, showing it only when it's unbearable to contain it anymore. Yet we are aware that it is there.
Robert DiNiro in Raging Bull, Jack Lemmon in Glengarry Glen Ross.

Okay, once again, if the character is supposed to be vulnerable in the scene then it's fine. But why would an actor actually be vulnerable because of what the other actors are doing? Like I mentioned above, Ang Lee isn't talking about acting vulnerable or awkward on purpose because the part requires it... it's talking about actors actually being vulnerable or awkward in parts that may or may not require it. And I can't for the life of me, despite all the people who get it explaining it to me, understand why if your fellow actor says a line or interacts with you, you'd actually feel hurt in real life and not play the part to the best of your ability. Do they not realize it's a movie? If you're supposed to play a calm and cool type character and you as an actor, not the character you're playing, can't restrain yourself emotionally, I don't get why anyone would want that?

OK, maybe I emphasized just one part of vulnerability too much, the 'crack in the tough exterior.' I'll try again.
When we apply for a job, we put every ounce of our being into looking and sounding good. We present our best self. We ACT.
When a new actor is playing his part, he too often tries too hard to act, while leaving himself behind. Of course that's the whole idea of acting, isn't it? Immerse himself in the character, study it, visit places and people who are that character in real life, like riding around with cops to play a cop?
No, I think says Lee, it isn't that so much, because then the actor loses something of himself. Meryl Streep is to me the pinnacle of never losing herself, no matter how adaptable she is to a character. That's a wider notion of vulnerability, I think. That way they are never two dimensional. No matter how good they are at 'being' a character, they shine through. Without trying to hide perfectly human flaws and be perfect, their acting becomes more natural, and together with the other skills of acting, it can all be perfectly imperfect, imperfectly perfect. Forget the words. It's what feels right to the viewer, who really does see himself, or someone he's close to, and identifies with.

I just looked back at this from you - 'Okay, once again, if the character is supposed to be vulnerable in the scene then it's fine.'
That is waaaaaaaay off track.
Either I'm not explaining well, or you just have very concrete ways of interpreting, or both - or something else, LOL.

Maybe what I should have said all along is that we ALL have vulnerability! Most of us put a lid on it, most of the time!

Different people look for different things...usually what they want to see...As far as actors go....most really aren't all that.

Some appear to be playing the same part as any other movie....the words and costumes differ...

A small handful..actually do change for the part they play. And that makes them a lot better..even if it doesn't make them more famous.

How is it way off track? The article is saying that it’s good for actors (not the characters the actors are playing) to be vulnerable or have insecurities or flaws. And I was just saying that if the character is supposed to be vulnerable then it’s not a problem if the actor is vulnerable. However if the character is supposed to be bold and heroic, I don’t get how the actor being vulnerable is a good thing. Perhaps you think the word vulnerable has a different meaning than I do hence I’m not able to understand

With all due respect, when I see a movie with Meryl Streep in it, I don’t want to see Meryl Streep. I want to see the character. That’s the biggest problem I have with actors like will smith. He always plays himself in every role. Whenever referring to his character in whatever movie, I always just say will smith. Actors like Gary oldman are great because you completely forget it’s gary oldman and you recognize him as the character he’s trying to play. So why is losing a part of yourself when doing a performance a bad thing and why is it good to be vulnerable/act like yourself when you should be playing someone else