This is what Tina Plank writes:

When eccentric viewing is working well a person has chosen and uses an area outside the central visual field loss. Training can help to stabilize fixation with this new area, thus enabling or facilitating daily visual tasks like reading or directing their gaze at objects of interest. People thus are able to regain some independence and usually report positive effects on their quality of life.

Eccentric viewing training and a more stable eccentric fixation are also associated with an enhanced processing of visual information in the brain. During eccentric viewing training, it could be shown that an improvement in fixation stability was positively correlated with an increase in brain activation (Rosengarth et al., 2013). This was observable in areas of early visual cortex as well as in higher areas of visual processing that play a role in object or face recognition. Further, in a visual search task a highly stable eccentric fixation was associated with higher performance and also with a task-related increase in activation in visual cortex (Plank et al., 2013).

References:

Plank, T., Frolo, J., Farzana, F., Brandl‐Rühle, S., Renner, A. B., & Greenlee, M. W. (2013). Neural correlates of visual search in patients with hereditary retinal dystrophies. Human brain mapping, 34(10), 2607-2623.

Rosengarth, K., Keck, I., Brandl-Rühle, S., Frolo, J., Hufendiek, K., Greenlee, M. W., & Plank, T. (2013). Functional and structural brain modifications induced by oculomotor training in patients with age-related macular degeneration. Frontiers in psychology: Perception Sience, 4, 428.

Here is a scientific presentation given by Tina Plank and others about how the visual cortex is reorganized with eccentric fixation training. See it as a complement to the film in which Anton Blomberg and Tina Plank discuss training a different area of the retina when central vision is destroyed.

A scientific article is also included in addition to this presentation.