In order to generate a flat map, features on the spherical Earth are projected onto a surface. To create this map, the shapes of the continents, along with latitude and longitude lines, were projected onto a cylinder. Then the cylinder was split and flattened. This type of projection is called a Mercator projection.
You can visualize the process of "projection" for this map by imagining a light shining at the center of the sphere, and considering the cylinder around it as a screen. Lines and shapes projected onto the screen by the light become the flat map.