The term 'shrinking' planet is another way of referring to the process of globalisation, or the deepening and strengthening of ties across transnational borders. This manifests itself in two main ways - goods and services, and can range from increased aircraft efficiency to international money transfers.
In the past, the world was a lot less connected. It would take months by ship to reach what we know now as the USA, and many months to produce a single Ford Model T car. Thanks to technological advance and increasing wealth, we can now find low-cost flights to other continents, exotic foods from countries previously unheard of, and we can hear languages completely different from our own.