"Ivy" is a shortened form of the term Ivy League, usually used in the plural ("the Ivys" or "the Ivies") to refer to the group of Ivy League universities. Often used in the context of intercollegiate sports, as can be seen in the examples below. Pretentious alumni will often ask questions like "Which Ivy did you attend?" and then scoff if you answer Penn or Brown, or worse yet, a non-Ivy like Bucknell.
Some useage examples from The Daily Pennsylvanian:
"Penn finished with its first winning season since 1996, but slid against Ivy teams."
"It's obviously disappointing to win only one match in the Ivies and have that one be against the weakest team."