three-way handshake

The agreement that opens a TCP connection: SYN from the client, SYN-ACK from the server, ACK from the client. The second message carries more proof than the other two combined — receiving it establishes at once that the server exists, that a program is listening on that port and accepted, and that the return path works. None of your data moves before all three, hence the cost of one round trip before the first byte. What it never proves is the application: a server answering an error completed exactly the same three messages as a healthy one.