There could be many answers to respond why computational neuroscience is so interesting now days. A sound example of the level of interest could be the Brain Initiative from the National Institutes of health, which states as a main research goal to seek new ways to treat, cure, and even prevent brain disorders. At some time in the future, we will be able to know better how to dismiss and prevent effectively mental illness like Alzheimer, Parkinson, and schizophrenia.
Computational neuroscience is becoming instrumental to achieve one of the next frontiers of the science: the complete understanding of how our brain works. This knowledge will constitute indeed an historical milestone that compares to the discovery of the quantum mechanics or DNA. The result will be a better understanding of our reality, an improved development of artificial intelligence technologies and a huge impact in our society and the way of living. (I would say it would also create philosophical and spiritual effects).
In the quest to know and understand the brain internals, the best scientists of the world, as well as researchers and great minds in so diverse areas like philosophy, cognitive psychology, cognitive science, neuroscience and psychiatry have formulated over time, better-refined theories, explanations and models.
As an example, in the field of cognitive psychology (which I like), there has been a steady progress and practical applications in psychotherapy and ergonomics. The cognitive psychological models of attention, perception, decision-making and memory have demonstrated to be very useful, but at an outer level. Computational neuroscience and computational psychology will allow us to produce better models and to know the inner working of the mental process, emotions, morality, decision-making, problem solving, and creativity and more.
On the other hand the integration of deep learning and machine learning are converging , where the complexity of machine learning algorithms are getting closer the brain computational models. We will see at some time in the future a resembling of artificial intelligence with the brain. Even scientists at IBM have claimed a computational breakthrough after imitating large populations of neurons for the first time.
The computational neuroscience is in that sense just a new line of research, which make use computational and mathematical models, based on the metaphor of the brain as an information processing apparatus. The growing number of research papers, journals, books, research centers, their inclusion as part of the college curricula, shows the importance of this area of study. All the cognitive and computational areas that exist today (there are many) therefore will continue complementing and reinforcing each other to achieve the goal: the complete understanding of how our brain works.
 Marblestone AH, Wayne G and Kording KP (2016) Toward an Integration of Deep Learning and Neuroscience. Front. Comput. Neurosci. 10:94. doi: 10.3389/fncom.2016.00094