They are called "windrose lines" and having a lot of them results in a "windrose network", and their purpose is to help in navigation, as if you follow that line, you get to where you are going.

The reason they are used is because of the big challenge with mapping a round earth onto flat paper. Nowadays, we understand a lot of these issues better, and we use projections to transform our spherical earth onto a flat map. Most early navigational charts, however, did not have projections, and instead used these windrose networks to establish connections between places. Because the earth is round, if you aren't travelling directly east or west on the map, the actual shortest path won't be straight if you draw it on a map. If you've ever flown internationally, you will often see how the plane's trajectory when flying from the US to Europe isn't directly east-west, but curves north over Greenland, because that is actually the shortest path over the spherical Earth. But that's really hard to calculate on a flat map. So the windrose networks were created to help sailors know the the best directions to send their ships, and to assist them with finding the correct bearings on the spherical earth from their flat paper charts. It's less a map of landmasses as it is a map of sailing directions.