Important Concepts
The primary abstraction provided is that of a UI states that form a Hierarchical State Machine. Informally, a state corresponds to a place in the overall application UI, and navigating through the application means moving ("transitioning" in state machine lingo) between different states.
A state can define one or more views that define the application UI for that state. A view definition specifies a template and associated controller (optional) to load into a corresponding ui-view directive, as well as dependencies to resolve and inject into the controller (also optional).
In the simplest case, the top-level HTML of the application will contain a single ui-view directive, and each state will define what to load into that directive when the application is in that state. However, a single view driven by a flat list of states is not enough for even moderately complex applications. The real power of these concepts comes from allowing views and states to be nested to form a hierarchy: The template loaded into a ui-view by a state can itself contain further ui-view directives that are then populated by child states.