I don't know why we say 'big head', but it is a common idiom. And it does not mean some REALLY has a big head (in size). It just means someone is very arrogant.
You might say, maybe in a work environment, 'His head is so big he won't fit through the door', to describe a very arrogant colleague.
We have another expression 'big wig'. This describes important people within a company, such as top management. I believe this expression comes from very long ago when the elite of Europe wore tall wigs.
Hope this helps. :)