An action is a message emitted by an instance of a UIControl subclass (a control) to notify you of a significant user event taking place in that control. The UIControl subclasses are all simple things that the user can interact with directly, like a button (UIButton), a switch (UISwitch), a segmented control (UISegmentedControl), a slider (UISlider), or a text field (UITextField).
The significant user events (control events) are listed under UIControlEvents in the Constants section of the UIControl class documentation; they also have informal names that are visible in the Connections inspector when you’re editing a nib. I’ll mostly use the informal names in what follows. Control events fall roughly into three groups: the user has touched the screen (Touch Down, Touch Drag Inside, Touch Up Inside, etc.), edited text (Editing Did Begin, Editing Changed, etc.), or changed the control’s value (Value Changed).
Apple’s documentation is rather coy about which controls normally emit actions for which control events, so here’s a list obtained through experimentation. Keep in mind that Apple’s silence on this matter may mean that the details are subject to change: