To learn more about a function, instead of browsing the source code, first look at the documentation. You can open it with `IGDocumentation[]`

and search for `IGPlanarEmbedding`

.

http://szhorvat.net/mathematica/IGDocumentation/#igplanarembedding

This function returns a planar combinatorial embedding of a planar graph. The “Planar Graphs” section of the documentation gives a brief explanation of what a combinatorial embedding is.

http://szhorvat.net/mathematica/IGDocumentation/#planar-graphs

As for *how* it works, it uses the LEMON graph library, which implements the Boyer-Myrvold algorithm.