Imagine you are drinking a glass of wine and a drop falls in the tablecloths (dishonor). The tableclothes, which we’ll call “complex plane”, now has a mark. The Conformal Map Theorem of Riemann says that if the mark has no holes, then it is “the same” as a circular mark. This “the same” is defined in terms of smoothness of how to move one mark into the other (you can imagine the tableclothes were plastic and you could actually deform the drop to get it circular). The smoothness and inversibility of thee movement ensures that you also respect angles in the process.
So, once you drop some wine, just put the glass back on top of the circle and nobody will notice!
Bernhard Riemann, German mathematician, born in September, 1826, had a huge influence in analysis, number theory and differential geometry. PS: please, don’t spill wine.