The global part here refers the simple fact that one cannot ignore the rest of the world nowadays, Or more precise: the earth - because at the moment human beings are restricted to the blue planet, with minor exceptions.
'Globalisation' is sometimes critizised as being the idea of politicians and global cooperations. But the main part of it is based on achievements that the western world always appreciated and that others have then adopted: The freedom of movement, and the prosperity and quest to use it. This mainly means the former east block and China. It extends to other regions like Africa, albeit under different conditions.
The global perspective does not mean we are expecting 'one world', some kind of unified society and culture living in harmony. To the opposite, globalisation involves a multitude of cultures for regions, nations or communities where the identity of each entity depends on a shielding of properties from the outside - they have to remain complex to each other.