Steming from its literary definition, in LOOKING AT MOVIES: by Richard Barsam & Dan Monahan, NY: W. W. Norton & Company 2009. 3rd Edition, "cinematic language" is the combination of methods, strategies and skills that filmmakers choose to convey the central message and the main ideas of the story that they are trying to tell.
It is basically the same notion as storytelling: the narrator chooses the tone, atmosphere, and style with which to tell the story in order to provoke in the listener empathy and emotion.
Similarly, a filmmaker understands how to perfect the manipulation of the scene through cinematic timing, transitions, and effects that would convey similar feelings in the viewer. This is also done through explicit and implicit meaning. The explicit meaning will directly show the audience a specific scene and relate exact information. The implicit meaning allows for the audience to formulate its own opinion about what they see. It is this interaction between the film maker and the audience which deems a movie to be successful.
This way of communicating with the audience is quite influential because it helps to make the necessary connections that will increase the validity and plausibility of the plot. In turn, this increases the popular interest in the work of the film maker while establishing a reputation of worthiness and quality for the production team within the industry.