In their model brain, they build functionality for 10 different tasks. These tasks were chosen to model those tasks used in psych evaluations, cognitive experiments, etc, so that the model can be compared to experiments with real humans. Good scientific choice there.
The user must design the function that she wants. The program then finds a particular network that can implement the function. This is like when you need to pay 55 cents, and you have a bunch of change, you can pretty much find multiple ways to make 55 cents (2 quarters + 5 pennies, 9 nickels + 1 dime, etc).
So for each task, they find a minimal mathematical description of the task in terms of eye movements, visual stimuli. Then, they fit a neural network to that description. This part is interesting neither scientifically nor mathematically, as we have known for 20 years that neural networks are universal function approximators. Look it up on google scholar, this is textbook stuff.
What IS interesting is what happens when they try to build up a brain, putting all these tasks into the same large network. This part is novel: they find that as they implement more and more tasks, it becomes easier to do so because they can adapt already existing components (like Daniel Dennett's exaptation) for use in the new task. This is vindication of evolutionary theory but in the context of cognitive neuroscience. Pas mal, as they say.
But these kinds of details aren't obvious unless you have domain knowledge and you've seen Chris Eliasmith speak a few times, and you've thought, mmm hold on a sec, show me them equations. (which he doesn't usually do).