The value of the "On Behalf Of" fields will be used to populate the "sender" header. This header can be used to pass "Sender Id" and "Domain Keys" authentication. However, these technologies are generally considered obsolete, and are superseded by DKIM and SPF authentication which are automatically enabled for all MessageGears accounts.
When the sender header is present, some email readers may display additional information to the reader regarding the origin of the message. For example: