I can't find the correct reference to the first introduction of graph minor. There are plenty of strong results on minors (Kuratowski theorem, well-quasi-ordering by Robertson and Seymour, ...) and good introductory textbooks (by R. Diestel, B. Bollobas and others) but I have not found who first introduced the term and why.
I am writing a PhD thesis on games on graphs and I would like to have the correct historical reference while trying to have it nice and complete.
The original motivation for the concept would be very interesting as well - was it $K_5$ and $K_{3,3}$ minor exclusion for planar graphs, or something even older?