iphone and ipod touch uses mobile version of OS X.
Quartz 2D is a drawing engine could be accessed by any OS X application.
Quartz 2D uses Graphic Context which is similar to Device Context in ms windows GDI.
Quartz 2D is implemented in the Core Graphics framework.
i think the benefit of Quartz is PDF graphic context. it enables easily create PDF file.
i had many information on Quartz 2D in Apple Develope Center documents.
this link is one of those documents.
http://developer.apple.com/documentation/graphicsimaging/conceptual/drawingwithquartz2d/dq_overview/dq_overview.html#//apple_ref/doc/uid/TP30001066-CH202-TPXREF101
i have been learned much about Quartz by those documents.