Tern stores metadata about the image and messages during operation in objects described here. The overall data model looks like this:
The main class is Image and its derived classes. This class contains a list of type ImageLayer. ImageLayer contains a list of type Package. Image, ImageLayer and Package contain a property called origins which is an object of type Origins. This class is used to record notes while Tern operates on an image such as what tools were used to retrieve the metadata or if the filesystem is of unknown content. Origins contains a list of type NoticeOrigin which contains a string and a list of type Notice. The Notice objects are where messages get recorded. You can easily record a message in the origins property of the Image, ImageLayer and Package types of objects by using the add_notice_to_origins method which just adds a Notice object to the NoticeOrigin object containing the origin string you give it ("origin_str" is basically a string indicating where in the image or analysis stage an event that you want recorded occured).
You will also see a class called Template. This is an abstract base class used to make custom formats. To learn more see the documentation on creating custom formats.