Fork i guess everyone uses in their lives, it has one stick which has splitted in to four parts further. Similarly in SIP it is like from one call it is processed in to multiple endpoints. It is like if a person is calling you at SIP mobile phone, normally you will get the ring only there and if phone is not with you, you will miss the call.
With SIP forking, if you have activated this powerful feature, at a same time you will get the call on your mobile phone and as well on deskphone or a softphone. Both devices would ring at same time.
Now coming to your query about call flow in the network: can't tell you the architectural flow here, you can get it from Specs
- UE sends INVITE message to SIP Proxy Server
- The Proxy server has information on which multiple endpoints has configured, it has to deliver (fork) the messages and fork the INVITE message to each of endpoints.