The language of cinema is less about the lingo used on set, and more about the meaning behind every shot and lighting choice. Cinematic language has been developed gradually over a century, and every combination of lighting and framing in a film has been carefully selected in order to convey a certain meaning. The art of cinematography is to understand those meanings and convey them to the audience through a visual medium.
As they mentioned in the video, you can break this language down into typical rules and conventions, and you can read up on the various definitions of cinematic slang. There's plenty of resources online about cinematography basics, which I would recommend reading up on, but other than that, watch movies.
It sounds simple, but you need to be prepared to ruin movies for yourself forever. Don't watch a movie for its entertainment value; watch it, and analyse each scene careful. Try to determine the relationship between the characters, and the work out how the filmmakers have positioned the lights and camera in order to convey that relationship. The best films are built on subtext, with true meaning conveyed not by the words the characters say, but their performances and the way the camera is positioned can reveal a completely different scene.
For example, you could have two spies sitting on a bench, merely chatting about the weather. The text is innocuous. But if the camera is positioned at a low angle, or you begin a slow dolly in the meaning can change. You cut in on a small shift in weight, a subtle movement of a suit jacket, an ECU on a mouth, and suddenly your scene has taken on subtext, and your have begun to introduce tension into a scene. Its this type of meaning that is conveyed by the cinematography, and it's this meaning that makes up the language of cinema.