Using stacking groups is a way to create a relationship between fields such that one field will slide up or down or disappear if another field is left blank.
To use stacking groups, go to each field's "Stacking Groups" tab. The first time you go to one, you'll need to create a new group. Select "Add New" from the Select Group dropdown menu, and enter a name in the Group Name box. In the Group Action dropdown menu, select what you want fields to do if another field is left blank. Then click "Update Stacking Group." You'll now be able to select your new group in the "Member of Group" dropdown in each field's Stacking Groups tab.
The "Depends on" option is used if you need one field to disappear if another is left blank, for example if you want a telephone icon to disappear if a telephone number is left blank.
Here is a brief video that demonstrates the use of stacking groups: http://screencast.com/t/MgVD4GLEUcc
In this particular video, the client wanted to create a business card with images next to the various phone numbers (such as a car for a mobile phone) and have the images disappear if the field was left blank.
Note: Stacking Groups are available on form-based templates only. Stacking Groups and Field Scripting will also not work together. A field containing a field script and with Stacking Groups enabled will always be considered to contain a value.