NOTE: Email addresses are always kept under the strictest privacy on Gaggle Mail and NEVER shared with anyone.
The "Hide email address of members" option is to further hide member email addresses from other members of your group.
By default when someone sends a message to a group on Gaggle Mail the people receiving the message can see the name and email address of the person sending it. However in some circumstances people want to communicate without other members of the group knowing their email address. In this case the "Hide email address of members" option should be enabled.
This option only hides the sender's email address if they have a name registered with their group they should change this to an alias to preserve anonymity.
If you have any questions about this or other matters of privacy then please let us know.