The following macro assumes you're using a Checkbox Content Control titled 'Checkbox1' and, for the text to be shown/hidden, a Rich Text Content Control titled 'ConditionalText':
Code:
Private Sub Document_ContentControlOnExit(ByVal CCtrl As ContentControl, Cancel As Boolean)
With CCtrl
Select Case .Title
Case "Checkbox1"
ActiveDocument.SelectContentControlsByTitle("ConditionalText")(1).Range.Font.Hidden = Not .Checked
End Select
End With
End Sub
The code goes in the 'ThisDocument' code module of the document or its template.
With the checkbox checked, the content will be formatted as visible; unchecked, hidden. To reverse the options, delete the 'Not' from the code.
Do note that whether text formatted as hidden will remain visible - or even be printed if not visible - depends on how the user has their Word installation configured.