It is an image representation used for an action or depicts something related to the application.
AppIcon is the icon for application that appears on the device springboard (the default screen that consists of all the applications).
It is a high resolution image of app icon of size 512 x 512 or 1024 x 1024(recommended).
This small icon is used in searched list of application. It is also used in the settings screen where the features related to the applications are enabled and disabled. Enabling location services is one such example.
There is a list of standard icons that are specially made for use in the toolbar and navigation bar. It includes icons like share, camera, compose and so on.
There is a list of standard icons that are specially made for use in Tab bar. It includes icons like bookmarks, contacts, downloads and so on.
There are special guidelines for the size of each icon for different iOS devices. You can explore further on the icon guidelines in apple documentation on Human Interface Guidelines.