The Call Bridge Group feature on Cisco Meeting Server is an advanced optimization to avoid excessive distribution calls that requires the option of Accept Replaces Header in the SIP Trunk Security Profile in addition to the rerouting CSS.
Sometimes you didn't find a convincing explanations.
Using Wireshark and RFC 3891, let's explain it in a few lines and a simple chart call flow.
CMS2 has the conference named electoral meeting already active. A new user join the same conference by dialing president@republic.com and the SIP INVITE is sent to CMS2. Between CUCM and CMS1 the SIP DIALOG is identified with:
CALL-ID: 9a189380-10001-76e-93f492a@10.1.5.16
SIP to tag: 4b9b16c771eb4337
SIP from tag: 2132~74e80987-2d30-48f7-a1e5-50a557f5e04e-22019832
CMS2 send an incoming SIP INVITE with the replace header "Replaces: 9a189380-10001-76e-93f492a@10.1.5.16;to-tag=2132~74e80987-2d30-48f7-a1e5-50a557f5e04e-22019832;from-tag=4b9b16c771eb4337". This field contains the same CALL-ID + TO TAG + FROM TAG as with the previous SIP DIALOG btw CUCM and CMS1.
In other words this field indicates that the SIP dialog identified by the header field is to be shut down and replaced by the incoming INVITE in which it is contained. In the SDP, CMS2 includes its IP Address, audio and video ports so that the user will establish the media directly to CMS2 instead of going through CMS1 then from CMS1 to CMS2.
This is why we need the Accept Replaces Header option in the SIP Trunk Security Profile, without this option the CUCM will reject the incoming SIP INVITE with replace header and sends back a 403 Forbidden SIP message. According to RFC 3891.
Once this incoming SIP INVITE is accepted, the CUCM triggers a SIP UPDATE message to the new user to inform him that the SIP dialog is modified.According to RFC 3311.