The role of the audience in a performance is partly one of consumer. The audience is the consumer of the product, in this case a play or a movie - in music it could be a concert, show or opera.
The audience is the body of theatre-goers the playwright had in mind when he/she wrote the play. This can vary widely from what one might think - and through history. For example, Shakespeare had to keep in mind the monarch (Queen Elizabeth was very different from King James who had an interest in witches and withcraft.) Sometimes plays were commissioined with the sole purpose of pleasing/entertaining a monarch, and then went public or on tour afterwards. Sometimes plays are popular with an audience segment the author had never envisaged.
A more mdern example would be 'Educating Rita' by Willy Russell. This play 'went down a storm' in a country where the class system and educational injustices were gradually being worn down partly through a more socialist attitude to education.
The role of the audience could also be to encourage the actors through their appreciation and applause.
The audience also acts as a barometer for public opinion about the play. In our contempoarary world, most plays are staged to generate revenue. It doesn't matter what the critics think...if no-one wants to go see it, the show will dive and close.
So many times in old movies, the actors who were playing actors would complain of "a dead audience" or they would remark, "What was with that crazy audience?" So, realistically, there must be a dynamic between actors and audiences. This is probably most salient with comedy. If the actors in a comedy, or the comic on stage do not make their audiences laugh, then the performance is a failure, as nothing returns to the comedians, and they realize that their comic performances are not generating the response that they should.
Essentially, then, the audience is a receptor of the stimulating agents on stage. Then, as part of the dynamic between audience and those on stage, the audience also transmits energy and responses to the actors. Thus, a receptive audience can improve the performance of those on stage; the responsive audience is absolutely essential to the success of those on stage.
The role of the audience can be variable in a performance. Like the second answer, the audience can participate. For instance, there have recently been some productions that play with this. The broadway shows, Momma Mia and Tina and Tony's Wedding experiment with this. For the later, the play is put on as if the audience was invited to a wedding and reception. There are also hybrid model that blur the distinction, like the play, Putnam County Spelling Bee. In part you are the audience, but at times you may participate.
There is another perspective that says the audience shapes the performance. In other words, the writers and producers are thinking about the audience when they are putting a performance together. In this sense, it is all about the audience. They exert an invisible power even before the performance.
On a high school stage, young actors are moved and motivated by an engaged audience. I've seen it happen time after time; the audience responds positively early in the show, and the show kills. I'm always most proud of my cast when the audience wasn't particularly demonstrative yet they gave the same performance they would have for a responsive audience. On a professional stage, I would expect that. For young people who are still concerned about being accepted and affirmed, the audience is critical. As a director, I like to sit in the back of the house and watch the audience because their experience is the major reason for the performance.
In addition to the audience in the traditional role of consumer is the newer, comtemporary idea of the audience as an actor. I am thinking of the Rocky Horror Picture Show where the audience functions as performers as well. In addition, there are other more interactive forms of "performanace art" which encourages the audience to be involved.
Bell Hooks wrote a lot about the capitalist, consumer-society and how it has influenced education as well as other spheres of life in a negative manner by making people passive. Paulo Friere was Bell Hooks' teacher who also wrote about consumers.
The audience actually is a very important part of basically any performance, whether it be a concert, a play, a musical, or something else. Many times performances require audience involvement, which leads to the performers realizing what is good and what is bad based on the feedback. Also, without the audience, performances would never make any money. And audience is needed to purchase tickets and get the word out about the performance.
The audience is there for performances because when you perform you would like people to watch you. Audiences are for telling you how you did and giving feedback on what you did good in the performance and what you need to improve on.
People can create as much music as they like, but without the audience, there is no feedback, no motivation/influence, and no means of support. With the audience, the performers are more likely to feel the optimism of the audience's support with their cheers and this causes the performers to give out their best whilst on stage.
This topic reminded me of a time when I went to the theatre to see "The Glass Menagerie". It was a time when I became self-conscious as a part of the audience.
I was quite young at the time, in my early twenties. If you have seen the play, you will recall how the mother is constantly yelling at her daughter, as she plays with her little glass figures. I had never seen the play before and when the audience laughed, I laughed along with them just caught in the audience response.
Of course, there is much more to this mother-daughter relationship being revealed here, and none of it was funny.
The lady sitting next to me said in a very loud voice, "Audiences are so stupid."
I never laughed again in the whole play. It wasn't a comedy, but audience response can be infectious.
Just to add on to things, please have a look at what is called 'Reader Response Theory'. With theories of poststructuralism, there has been a serious interrogation of the authorial function in a text in terms of intention and meaning. It started with American New Criticism and culminated with Foucault's talk What is an Author? or Barthes's The Death of the Author. Death of the author has led to a new rebirth of the reader, as Barthes says.
The audience in a dramatic performance or the reader of a text is seen today as the meaning-maker. It is they who construct a text as much as the author or the playwright. The meaning of performance is like a meaning initiated by the dramatist, mediated by the actor and the director and left open until it is completed in terms of the response of the audience.
Brecht talked about 'Alienation-effect' to draw attention to the illusory nature of theatre; theatre as theatre and not reality. In poststructuralist terms, this is what is known by 'defamiliarization'.
Dramatists like Peter Handke have made plays out of audiences like Offending the Audience. The work of Stanley Fish, Wolfgang Iser are important theorists in the field.