This number sets the margin between the left and right edges of your buttons and the text within them. The default is "none." With top-buttons, this number also determines the page width.
Here are examples of Button-padding set at 0 and at 30. Increasing this number increases overall button width.
Button-padding set to 0:
Button-padding set to 30:
Please note: If your Store uses top-buttons, the width of the page is determined by the size of the buttons. In this case, you can use Button-padding to control page width.