No, we don’t know totally how the brain works. There’s a lot of big questions about it we don’t know, such as: how does our memory work? what gives us our personalities? what is consciousness? why do we sleep and dream? is the brain like a computer…could we engineer one?
We can understand that different areas of the brain are responsible for memory, sight and personality etc. However, we don’t know how the variation in each of our abilities to perform is managed (i.e why I am better at science and my friend is better than me at learning language).