I was wondering this too, Daniel Wilson gathered the documentation, but to the untrained eye it doesn’t mean much. Here’s what it’s all about: “extract mode” is referring to the type of view that’s shown when the space is too small, for example landscape on a phone. I’m using Galaxy S4 with Google Keyboard as input method editor (IME).
Landscape UI without visible IME
Based on the focus (on Description) you can see TextInputLayout in action pushing the hint outside the editor. Nothing special here, this is what TextInputLayout is supposed to do.

Landscape UI editing empty Name field
Editing the Name you can see that the IME doesn’t give you a hint of what you’re editing.

Landscape UI editing empty Description field
Editing the Description you can see that the IME gives you a hint of what you’re editing.

Layout XMLs
The difference between the two fields is their type EditText VS TextInputEditText. The important thing here is that TextInputLayout has the android:hint and not the wrapped EditText, this is the case when TextInputEditText‘s few lines of Java code makes a big difference.
Name field
<android.support.design.widget.TextInputLayout
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:hint="Item Name"
>
<EditText
android:id="@+id/name"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
/>
</android.support.design.widget.TextInputLayout>
Description field
<android.support.design.widget.TextInputLayout
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:hint="Item Description"
>
<android.support.design.widget.TextInputEditText
android:id="@+id/description"
android:layout_width="fill_parent"
android:layout_height="wrap_content"
android:inputType="textMultiLine"
android:minLines="4"
android:scrollbars="vertical"
/>
</android.support.design.widget.TextInputLayout>