Huge question - and one about which people have written entire books. When it premiered on the 8th May 1956 at the Royal Court, "Look Back" caused uproar - it opens, of course, with Alison Porter doing the ironing, and at the sight of an ironing board, the audience gasped.
The prevalent style before "Look Back" might be best seen by comparing it with another popular play from the period ("The Chalk Garden" by Enid Bagnold might be a good place to start) - but they tend to be set in drawing rooms, to be classified usually as comedies, and to focus on upper-class characters.
John Osborne actually started the movement with "Look Back" that came to be known as the "Angry Young Men" - who brought writing which, like Osborne's play, sparkled with energy and determination, eschewed politeness, and sympathetically depicted middle-class characters realistically - ironing boards and all!
Though critics like Dan Rebellato have since argued otherwise, the premiere of "Look Back" is traditionally seen as the beginning of the "Angry Young Men" movement in British Theatre.
Even though "Look Back in Anger" was written in the standard 3-act, realistic form, it was ground-breaking in terms of the content and themes. John Osborne, out of Britain's "Angry Young Men" movement, wrote a play that featured a character that was angry with society. Prior to this play, most plays of the time (1956) were well-mannered and didn't deal with harsh subjects. One of the themes that Osborne's play deals with is the struggle between the classes and the anger that the lower classes feel at being misunderstood by the upper classes.
The critical success of the play led other playwrights to write plays that more realistically mirrored the world around them.
On its first staging in 1956, Osborne's play Look Back in Anger definitely looked like an example of revolutionary theatre, primarily because of its angry young protagonist, Jimmy Porter. As a representative of the young generation of 1950s, Porter was the unique proprietor of tirading anger directed against the upper classes and the institutions like the Church, the Press, the Education etc. The play initiated the genre of the Theatre of Anger with Porter as a Hamlet like figure to feel and express that the time was 'out of joint'. Osborne's play looked into the hypocrisies of a class society, into the man-woman relationship, questions of friendship, sexuality, politics & so on , making deliberate use of a shocking and slangy language.
However, from the early 1960s, the play came to be seen as an example of a well-made play which fails to go beyond anger and resentment, ending on a note of sentimental reconciliation of Jimmy and his upper-class wife Alison. The political implications of Osborne's play have since then died down.