Answer by Jay Wacker:
The name "Ivy" refers to the ivy growing on the walls of the buildings of universities, particularly in the northeast. In the mid-to-late 19th century, the name "the Ivies" became a catch phrase for a wide cadre of universities in the northeast, including many that are not part of the current Ivy League. Stanford was just being founded when this name was really in vogue. The term "Ivy" was then co-opted when collegiate athletics started to formalize and leagues were formed. The strict term "Ivy League" has always been an athletic conference, going back to its inception in the 1930s. Athletic conferences were local since travel was prohibitively difficult at the time. Stanford is not exactly next door to the current Ivy League schools and therefore wouldn't be in the same athletic conference as east coast schools.