what's Nuero-linguistics?

Is the interdisciplinary study of language processing in the brain, with an emphasis on the processing of spoken language when certain areas of the brain are damaged. It also describes the how our bodies function and language determines how we interface and communicate with other people. It  involves strategic thinking and an understanding of the mental and cognitive processes behind behavior.

What could learning language and teaching benifit from nuerolinguistics studies?

As a matter of  fact, the brain does not issue motor commands one segment at a time... when we consider the whole range of factors that affect the timing of speech events (such as breathing rate, the movement and coordination of the articulators, the onset of vocal - fold vibration, the location of stress, and the placement and duration of pauses). It is evident that a highly sophisticated control system must be employed, otherwise speech would degenerate into an erratic, disorganized set of noise.(David Crystal 2010)