Also, if such an actor was storing encrypted traffic as well, they could now easily decrypt this traffic en mass.
This is called Forward Secrecy.
Without forward secrecy, the client chooses the premaster secret, encrypts it with the server's public key, and sends it in the ClientKeyExchange message. With forward secrecy, the client receives signed ServerDHParams in the ServerKeyExchange and responds with ClientDiffeHellmanPublic in the ClientKeyExchange.