How did the voyages of exploration connect the world's continents?

Imagine the world as a giant puzzle with the pieces scattered far apart. For most of human history, each piece kept to itself. People in Europe had never tasted a potato. People in the Americas had never seen a horse. Then, about five hundred years ago, sailors began stitching the pieces together with nothing but wooden ships and a lot of nerve.
Why bother sailing into the unknown at all? Mostly because of spices. Pepper, cinnamon, and cloves grew far away in Asia, and Europeans loved them. But the overland routes were long, crowded, and expensive. So traders had a wild idea: what if we could reach Asia by sea instead, and skip the middlemen entirely?
