The World 'Shrank' in the 1500s can be understood as follows
(i) Europeans discovered the sea route to Asia and so trade activities became increased between Asia and Europe.
(ii) The American continent was discovered only when the sea-route through the Atlantic Ocean to America was found.
(iii) Due to both of the above reasons, there was increased interaction among the people living in various continents of the world, thus causing the world to 'Shrink' in metaphorical terms.