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.

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    $\begingroup$ Note that as stated in the documentation, "Heads need not be symbols", e.g., FixedPointList[Head, f[x][y][z]] // Most returns {f[x][y][z], f[x][y], f[x], f, Symbol} $\endgroup$ – Bob Hanlon Sep 25 '15 at 21:39
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    $\begingroup$ An answer may be found in the first tutoria,l Everything Is an Expression, linked in the documentation for Head. $\endgroup$ – Michael E2 Sep 26 '15 at 1:30

Wagner's Power Programming with Mathematica begins chapter 2.1.1 thus:

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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.