The theory of a post-industrial society has a number of different dimensions, depending on the writer involved. Bell's argument ("The Coming of Post-Industrial Society", 1974) is different to Kerr et al's argument ("Industrialism and Industrial Man…", 1960) which, in turn, is different to the argument put forward by writers such as Fukayama ("The End of History?", 1989).
However, whatever the specific differences of emphasis and interpretation, the basic theory remains roughly the same; all societies are "inevitably" heading towards an economic, political - and probably, in the long run, cultural - convergence. In simple terms every society will come to share the same - or very similar - features to every other society. In broad terms, the argument is that post-industrial societies will be broadly democratic, Capitalist societies that display a great deal of cultural homogeneity (that is, similar forms of culture).
As you might expect, the motor of convergence is globalisation; in this respect, the globalisation of economics leads to global forms of politics and the spread of cultural ideas across different societies. We can see an example related to post-industrial forms of production in terms of the concept of "Post-Fordist" production techniques and organisations.