Distortions are a bit hard to explain but the general idea is that the world is like an orange skin - if you peel off the skin and spread it out (in one piece), then you have …the world and the distortions of maps laid out in front of you. We live on a big ball. Forcing the ball's image onto a 2-dimensional surface is the inevitable problem. Globes are the 'maps' that have the least over-all distortion, but in many ways they have far less detail and practical usefulness than well made 2-dimensional maps. Distortions are also known as projections. Over the years there have been arguments over which projection best explains and depicts the world and in the end, it resulted in the following different projections: .
Wagner VII Projection/Pseudo azimuthal projection .
Conic Projection .
Mercator Map .
And many more.... The importance of distortions very much depends on how a map will be used. If you are planning a country's defense systems and strategies, then you want to eliminate or be able to account for global distortions to the highest degree of accuracy. If you want a good road map that will get you to a destination a thousand miles away, global distortions will mean absolutely nothing to you. Political maps may or may not be improved by paying attention to distortions; sometimes relative areas of adjoining areas will be critical and sometimes not. There aren't going to be many border disputes among the states of the US; it might be different in other parts of the world. ( Full Answer )