A modal view controller is a mechanism for managing a modal view, i.e. a view that assumes logical control of the user interface until the modal view is dismissed.
A modal view is a user-interface view that interrupts and existing workflow in order to present information to, and/or solicit information from, the end-user. A modal view generally assumes logical control over the user interface, and does not yield the user interface back to the presenting workflow until the user dismisses the modal view. Modal views generally represent some self-contained process or set of information that must be completed before dismissing the modal view and allowing the application's broader workflow to continue.
A "modal view controller" is a view controller that manages a modal view.
Apple-specific references:
Definition of a modal view.
View Controller Programming Guide has a broader discussion of view controllers.
Presenting Another View's Content in the UIViewController Class Reference enumerates the various methods for transitioning to a view controller modally, governing the particulars of the modal transition, and the process for dismissing a modally presented view controller.
