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from __future__ import print_function
    
The ButtonWidget is not used to represent a data type.  Instead the button widget is used to handle mouse clicks.  The on_click method of the ButtonWidget can be used to register function to be called when the button is clicked.  The doc string of the on_click can be seen below.
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from IPython.html import widgets
print(widgets.ButtonWidget.on_click.__doc__)
    
Since button clicks are stateless, they are transmitted from the front-end to the back-end using custom messages.  By using the on_click method, a button that prints a message when it has been clicked is shown below.
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from IPython.display import display
button = widgets.ButtonWidget(description="Click Me!")
display(button)
def on_button_clicked(b):
    print("Button clicked.")
button.on_click(on_button_clicked)
    
The TextWidget also has a special on_submit event.  The on_submit event fires when the user hits return.
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text = widgets.TextWidget()
display(text)
def handle_submit(sender):
    print(text.value)
text.on_submit(handle_submit)
    
Widget properties are IPython traitlets and traitlets are eventful.  To handle  changes, the on_trait_change method of the widget can be used to register a callback.  The doc string for on_trait_change can be seen below.
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print(widgets.Widget.on_trait_change.__doc__)
    
Mentioned in the doc string, the callback registered can have 4 possible signatures:
Using this method, an example of how to output an IntSliderWiget's value as it is changed can be seen below.
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int_range = widgets.IntSliderWidget()
display(int_range)
def on_value_change(name, value):
    print(value)
int_range.on_trait_change(on_value_change, 'value')