In the old times people died a lot more than they do today, and many had various accidents. From the way people died or the way they were affected by accidents they were able to roughly deduce the role of each of our organs and what they do and how they affect us. Doctors did exist and they did examine patients post mortem as well as attempt surgery, with varying results. Also the same applied to animals, and people were able to understand that animals such as deer or livestock had the same organs as us so this allowed for further observation and experimentation.

Overall while there may have been several misconceptions and mysteries throughout history a surprising amount was understood about our bodies. Figuring out that the brain in particular is the center of thought and sense of self is relatively easy since they could easily observe how injury to the brain or other ailments like tumors could affect one's faculties.