What the handshake achieves

TLS 1.3 handshake (1-RTT)

Client                                          Server

ClientHello
  + key_share
  + supported_versions
  + signature_algorithms          ───────────►

                                                ServerHello
                                                  + key_share
                                                {EncryptedExtensions}
                                                {Certificate}
                                                {CertificateVerify}
                                                {Finished}
                                  ◄───────────  [Application Data]

{Finished}                        ───────────►
[Application Data]                ───────────►  [Application Data]

Notation:
{}  = encrypted with handshake traffic key
[]  = encrypted with application traffic key

By the second flight, the server is already sending encrypted application data. With a session resumption ticket and 0-RTT data, an established client can send a request in the very first flight — though 0-RTT data has replay considerations.

What changed from TLS 1.2

TLS 1.2TLS 1.3
Round-trips2-RTT1-RTT (or 0-RTT with resumption)
Cipher suite size~300 combinations5 AEAD-only suites
RSA key exchangeAllowedRemoved — only (EC)DHE
Forward secrecyOptionalMandatory
Static RSA, CBC, RC4, SHA-1, MD5AllowedRemoved

Key concepts