The information society is a new kind of society. Specific to this kind of society is the central position information technology has for production and economy. Information society is seen as successor to industrial society. Closely related concepts are post-industrial society (Daniel Bell), post-fordism, post-modern society, knowledge society, Telematic Society, Information Revolution, and informational society (Manuel Castells).
The term information society is a translation of the Japanese jôhô shakai (情報社会, Umesao), which means the highest stage of societal evolution seen in analogy to biological evolution. This concept was discussed already in the 1950s and 1960s. 
There is currently no universally accepted concept of what exactly can be termed information society and what shall rather not so be termed. Most theoreticans agree that we see a transformation which started somewhere between the 1970s and today and is changing the way our societies work fundamentally. Information technology is not only internet, and there are discussions how big the influence of specific media or specific modes of production really is.
Considering that metaphors and technologies of information move forward in a reciprocal relationship, we can describe our society (and more specifically the Japanese society) as an information society because we think of it as such (James Boyle, 1996, 6).
One issue which makes information much more important than before is the integration of photography, film, etc. with the computer; which moves gradually from being an universal machine to being an universal media-machine. Another important issue is the close relation between information technology, modes of production and globalisation.
Caveat: Information society is often used by politicans meaning something like "we all do internet now"; the sociological term information society (or informational society) has some deeper implications about change of societal structure.
See also: World Summit on the Information Society (WSIS)
The Information Society is also the title of an sociological journal, founded 1981, which defines itself as an "critical forum for leading edge analysis of the impacts, policies, system concepts, and methodologies related to information technologies and changes in society and culture" (homepage).
Information Society was also a musical group, see Information Society.