Added explanatory comments.

first_screen.kv

@@ -5,7 +5,7 @@
             text: 'This is the first screen.'
         Button:
             text: 'This button prints a number.'
-            on_press: root.print_number()
+            on_press: root.print_number()  # In a custom widget's Kv, `root` refers to the custom widget.
         Button:
             text: 'Change…'
-            on_press: app.open_second_screen()
+            on_press: app.open_second_screen()  # But `app` still refers to the application object.

first_screen.py

@@ -3,7 +3,7 @@ from kivy.uix.screenmanager import Screen
 from kivy.properties import NumericProperty
 
 
-Builder.load_file('first_screen.kv')
+Builder.load_file('first_screen.kv')  # Because this is not the main app Kv, we must load it explicitly.
 
 
 class FirstScreen(Screen):

main.py

 from kivy.app import App
 
+# The following lines ensure that FirstScreen and SecondScreen are available for when the Kv code is loaded.
+
+# Because neither PyCharm nor PyLint are aware of the associated Kv, we must disable their warnings about these widgets
+# not being used.
+
 # noinspection PyUnresolvedReferences
 from first_screen import FirstScreen  # pylint: disable=unused-import
 # noinspection PyUnresolvedReferences

second_screen.kv

@@ -4,7 +4,7 @@
         Label:
             text: 'This is the second screen.'
         Label:
-            text: root.message
+            text: root.message  # In a custom widget's Kv, `root` refers to the custom widget.
         Button:
             text: 'Change…'
-            on_press: app.open_first_screen()
+            on_press: app.open_first_screen()  # But `app` still refers to the application object.

second_screen.py

@@ -3,8 +3,8 @@ from kivy.uix.screenmanager import Screen
 from kivy.properties import StringProperty
 
 
-Builder.load_file('second_screen.kv')
+Builder.load_file('second_screen.kv')  # Because this is not the main app Kv, we must load it explicitly.
 
 
 class SecondScreen(Screen):
-    message = StringProperty('Hello, World!')
+    message = StringProperty('Hello, World!')  # This property is changed by twoscreen.kv.

twoscreen.kv

@@ -5,4 +5,4 @@ ScreenManager:
     SecondScreen:
         id: second
         name: 'second'
-        message: 'This is a message!'
+        message: 'This is a message!'  # The app sends information to the custom widgets by setting their properties.