This is one of the best videos out there explaining, quite simply, what map projections are and why they are so important. It has great graphics and touches upon the history of projections, which is always cool to know ;)
I hope anyone interested in cartography, GIS, or just maps in general finds it helpful :)
Video's by Johnny Harris and here's the website they mention in the video to compare and contrast the sizes of countries, taking into account projection distortion: http://thetruesize.com/