OCSP stapling is a way for the server to send proof that its certificate is still valid during the TLS handshake. This saves the client from asking the certificate authority directly, making connections faster. In nginx, you enable it with 'ssl_stapling on;' and 'ssl_stapling_verify on;'. You also set DNS resolvers so nginx can find the OCSP server. When a client connects, the server sends its certificate plus the OCSP response. The client checks both and if valid, the secure connection proceeds. The server refreshes the OCSP response regularly to keep it fresh. This process improves security and speed for HTTPS connections.