Look Back in Anger was a revolutionary play for the mid-1900s because it (1) was loaded with emotion, (2) represented the alienation of much of England's youthful population during a time of upheaval in the British Empire, and (3) cast a working class "bloke" as an antagonistic hero.
(1) The emotionality of the play was a shock to mid-twentieth century play audiences that were being presented (good but tame) plays like My Fair Lady, The Chalk Garden, and Mouse Trap. England was going through politically difficult times with post-World War II adjustments and the loss of much of the British Empire as colonial holdings were gaining independence. (2) Osborne's play was believed to express the same anger and frustration felt by England's youth who were locked in by antiquated class divisions and limitations.
(3) Previous plays had cast working class male characters but they had previously filled the role of comedic relief, sort of the Shakespearean Clown of the then modern day, who would misuse language and be held back by their inability to be articulate. Jimmy Porter, however, though a working class young man, is college educated, albeit at a low prestige new "white tile" university, and is intelligent and articulate and, therefore, must be taken seriously. This is what most revolutionized Osborne's play, the elevating of the persona, emotions and articulate abilities of a working class hero.
The form of the play is "old-fashioned" because it follows the established three act plot structure that had worked so well for such as Henrik Ibsen, Tennessee Williams and others. Osborne's basic plot device is also a classical one, that being a love triangle in a marriage rankling with malice, just like Jimmy himself rankles in malice. Further, the basic structure of the plot is standard and in fact has some clumsy bits, such as the coincidence of Cliff's exit and re-entrance and the placement of the phone calls. Some critics think these are smoothed over by the revolutionary dialogue language and passion.