Attribute Visibility
Clicking the 'attribute visibility' link next to a group will take you to the Group Attribute Visibility page. Here you can specify which of your attributes are visible to users within the current group.
There are 3 choices available for each attribute: 'Not visible', 'Visible when viewing', and 'Visible when editing and viewing'.

So it is simply a case of going through each of your attributes and selecting if and when they are visible to users in the current group.
Note: The 'Visible when editing and viewing' option will not be available for attributes that are not editable (eg. 'ID' or 'Date Created').
Note: that if a user is a member of another group for which an attribute has a higher level of visibility then that takes priority, and the user will be able to see the attribute.