SSL_accept() is the server-side OpenSSL function that starts and drives a TLS handshake. It is called when a server is ready to negotiate encryption parameters with an incoming client, before any application data is exchanged. During this phase, OpenSSL parses handshake messages, chooses cipher settings, and sets up keys for the secure session.
This function matters because it sits at a trust boundary. If handshake processing mishandles attacker-controlled input, a remote client may trigger excessive memory use, crashes, or other pre-authentication failures before login or certificate checks complete. In attacks, that can be used for denial of service against web servers, proxies, VPN gateways, and other TLS-enabled services. In defense, administrators look for vulnerable OpenSSL builds, patch quickly, and monitor for repeated incomplete handshakes, memory spikes, and abnormal restarts on TLS listeners.