No, you probably have not seen the term Altermodern before. It is created for the Tate Britain's current Triennial Exhibition celebrating current trends in British art. It is the title of this exhibition.
According to the exhibition guide, the curator, Nicolas Bourriaud, is "proposing the new term 'altermodern' to describe how artists are responding to the globalized world in which we live."
Further, "'ALTERMODERN' is an in-progress redefinition of modernity in the era of globalization, stressing the experience of wandering in time, space and mediums. The term 'altermodern' has its roots in the idea of 'otherness' (Latin alter = 'other', with the English connotation of 'different') and suggests a multitude of possibilities, of alternatives to a single route. It suggests that the historical period defined by postmodernism is coming to an end, symbolised by the global financial crisis. But what era are we entering into? The times seem propitious for the recomposition of a modernity in the present, reconfigured according to the specific context in which we live--crucially, in the age of globalisation--and understood in relation to economic, political and cultural conditions."
Still further, "If twentieth-century modernism has mainly been a western cultural phenomenon, altermodernity arises out a negotiations between agents from different cultures and geographical locations. Stripped of a centre, it can only be polyglot. Altermodernity is characterized by cultural translation. The archipelago and its kindred forms, the constellation and the cluster, function here as models representing the ALTERMODERN. They present the figure of the artist as home viator, a traveler whose passage through signs and formats reflects a contemporary experience of mobility..."
Last paragraph: "ALTERMODERN art often functions as a hypertext, translating and transcoding information from one format to another. Artists wander in geography as well as in history, exploring a transcultural landscape saturated with signs to create new pathways between multiple formats of experession and communication."