How to generate board plot/image in Eagle
There isn't a way to do this directly in Eagle. That image was drawn in a graphical design package, not in a PCB editor. It's a cartoon, not a mechanical drawing.

About the farthest you can get is the DXF export capability in Eagle. If you show key parts such as the board outline, holes, and top silk layers, you can have Eagle save a DXF file which can be imported into a graphical editor (Corel Draw, Adobe Illustrator, GIMP, Inkscape, etc. {italics are free}).

The imported DXF file will be interpreted as a vector graphic, allowing you to easily edit it in your editor of choice. Tidy up and add the desired colourings.