What is the purpose of asceticism? Christians have been practicing asceticism for thousands of years. Why? I would prefer sources from before the Great Schism. If not are available I will accept Orthodox teaching from after that time.

For an example of the type of answer I am looking for, I will say that my current understanding regarding the purpose of ascetic practices is that engaging in them intentionally helps to turn the heart away from things like pride, gluttony, comfort, etc and toward God by willingly being humiliated, deprived, and discomforted in a repeated and systematic manner. Does that sound wrong?
It's sort of like you said:  Asceticism is the way to turn away from things of this world and turn toward God and become more like Him.  A good book to read that will likely help answer your question would be Early Christian Writings: The Apostolic Fathers.