I know (by practice) what a head is, but I am unable to find the appropriate words to actually define it. I would like to see a precise definition of head using the appropriate technical words involved. Hopefully, this should provide me with a better understanding of how Mathematica works.
Wagner's Power Programming with Mathematica begins chapter 2.1.1 thus:
The definition of head is its position in the expression. If you want to really understand expressions I encourage you to follow the link above to the answer here on Mathematica.SE where the book is available for free, and continue reading starting at the point I quoted.