Box and Pack by Group 

If the polys of the selected groups have been flattened already, then this button will place all the shells into boxes, a separate one for each group, and then packs them all automatically.

Detach 

All marked polys are detached, exactly as if you had moved the mouse pointer over them and typed the Enter hotkey.

Select 

If the marked polys have been flattened already, then the Select button will select those shells. This would allow you then for example to move all those shells off to one side for other processing.

Box 

Again, if the marked polys have been flattened already, then the Box button will gather all of those shells together into a Pack box.

Various methods can be used to select groups in the list:

LMB 

Selects just that group, deselecting all others. Click'n'drag to select multiple groups.

Ctrl-LMB 

Toggles that group, leaving all others as they are. Click'n'drag to toggle multiple groups.

Shift-LMB 

Selects all groups between this and the previous selection.

Collapsing a group list (i.e. clicking on Polygon, Material or Smoothing) will deselect all the groups in that list.

Editing

These buttons can be used to edit the group list and members.

New 

If no group name is selected, this opens up a text entry field where you can type in the name for a new group. Type the Enter key to save the name. Any G key marked polygons will be moved into this new group.

If a group is selected, this opens up a text entry field where you can edit the group name. Type the Enter key to save any changes.

Add 

This adds all G key marked polygons to a group in the list. Click the button first, then click on the group name. If those polygons were already in one or more groups, they will stay as members of those groups.

Move 

This moves all G key marked polygons to a group in the list. Click the button first, then click on the group. If those polygons were already in one or more groups, they will be removed as members from those other groups.

Del 

If no group name is selected, this deletes all empty groups from the list.

If a group is selected, this removes that group name from the list.