Question regarding volume 1

Hello people
I’ve been doing the security course ( loving it so far ) and I’m on the encryption crash course. It was mentioned the server communicates with the machine using first its public key to encrypt the session key ( symmetric key ) and then send it to the user for an extra security measure.

Where does the use of the private key of the server come in handy.
Also is it used in the digital certificate process

Thank you for your time

The sever encrypts the session key with its private key and the browser decrypts it with the public key. The certificate is used to authenticate the server is the genuine server.