Performance of a damaged brain I have heard stories/reports that if a certain part of the brain (taking care of certain functions) is damaged other parts take over the function of the damaged part.

Intuitively this could mean 2 things:


We are not using the brain to its full capability.
The performance of the brain will take a hit due to other brain centers taking over the functionality of the damaged center.


For me the first one does not make sense since evolutionary selection makes sure we are endowed with the most efficient systems. So what is happening exactly when brain centers get damaged?
To the question "what is happening exactly when brain centres get damaged?". The answer is: When any tissue, including neural tissue, in the body gets damaged, the body will try to repair them. The process of reparation involves many distinct processes, such as the process to get rid of the damaged tissue and the process to regenerate new tissue. But compared with other tissues, such as skin, mucosa, and connective tissue in general, neural tissue has a much more limited capability to regenerate, yet it is not zero. Also, in the nervous system, neural plasticity, which is the adaptation of other neural tissue to perform the function that is impaired or lost, plays the role in the process of reparation too. The following articles may help explain this matter in more details: ref1 and ref 2,  and ref3. And some animal studies of neural plasticity: ref4 and ref5.