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for my thesis I got handed a TeX template and I was trying to understand the code before doing anything redundant or useless. I got most of it figured out but then there's this piece of code I can't decipher:

makeatletter
 defthebibliography#1chapter*References@mkboth
 REFERENCESREFERENCESlist
 [arabicenumi]settowidthlabelwidth[#1]leftmarginlabelwidth
advanceleftmarginlabelsep
usecounterenumi
defnewblockhskip .11em plus .33em minus .07em
sloppyclubpenalty4000widowpenalty4000
sfcode`.=1000relax
makeatother

It's right before the bibliography.

Is anyone able to help me understand this arcane language?

With slightly different indentation the code reads

makeatletter
defthebibliography#1%
 chapter*References@mkbothREFERENCESREFERENCES%
 list
 [arabicenumi]
 settowidthlabelwidth[#1]%
 leftmarginlabelwidth
 advanceleftmarginlabelsep
 usecounterenumi%
 defnewblockhskip .11em plus .33em minus .07em%
 sloppy
 clubpenalty4000
 widowpenalty4000
 sfcode`.=1000relax
makeatother

It modifies the command thebibliography that forms the basis of the begin code of

beginthebibliography<longest label>
bibitem<key> <entry text>
endthebibliography

In detail

 chapter*References@mkbothREFERENCESREFERENCES%

First the code typesets an unnumbered chapter References and adds running heads on both sides reading REFERENCES.

 list
 [arabicenumi]

The bibliography is typeset as a list using the counter enumi (a bit unusual, the standard implementations use the counter enumiv, but normally that does not matter). The label number/label is wrapped in square brackets

 settowidthlabelwidth[#1]%
 leftmarginlabelwidth
 advanceleftmarginlabelsep
 usecounterenumi%

This is standard stuff that sets up a list with sensible margins for this scenario.

 defnewblockhskip .11em plus .33em minus .07em%

Defines the additional stretchable space that newblock inserts. newblock is a command issued by many bibliography styles to separate larger blocks of information in the bibliography. It allows for visual separation and can help improve line breaking with its additional stretchiness.

 sloppy

Sets parameters for line breaking, see What is the meaning of fussy, sloppy, emergencystretch, tolerance, hbadness?. This setting is usually good at avoiding overfull, but could give sub-par result for longer paragraphs of text. For the bibliography that is probably acceptable.

 clubpenalty4000
 widowpenalty4000

Sets parameters to control widows and orphans. See How do I prevent widow/orphan lines? and https://texfaq.org/FAQ-widows.

 sfcode`.=1000relax

Disable the larger space after sentence-ending .s in the bibliography. See also Double space between sentences.

Compared to the standard definition in report.cls (it's the same in book.cls and only slightly different in article.cls)

newenvironmentthebibliography[1]
 chapter*bibname%
 @mkbothMakeUppercasebibnameMakeUppercasebibname%
 list@biblabel@arabicc@enumiv%
 settowidthlabelwidth@biblabel#1%
 leftmarginlabelwidth
 advanceleftmarginlabelsep
 @openbib@code
 usecounterenumiv%
 letp@enumiv@empty
 renewcommandtheenumiv@arabicc@enumiv%
 sloppy
 clubpenalty4000
 @clubpenalty clubpenalty
 widowpenalty4000%
 sfcode`.@m
 def@noitemerr
 @latex@warningEmpty `thebibliography' environment%
 endlist
newcommandnewblockhskip .11em@plus.33em@minus.07em

we note the following differences:

• Your code only redefines the begin code (presumably the end code is left unchanged).


• Your code uses enumi instead of enumiv. In practice that difference should hardly matter.


• The standard code has customisable macros in some places where your code has hard-coded values ([...] vs @biblabel...; References vs bibname; ).
  
  
  • In particular the standard classes would print bibname, which defaults to Bibliography, while your code has References hard-coded. This is about the only visible difference between your code and the standard definition for 'normal use' (assuming the standard definition of def@biblabel#1[#1], which is hard-coded in your definition).
  
  


• Since your code redefines newblock in the begin code, all changes that are made to that command in the document will be void.

FWIW I found http://kb.mit.edu/confluence/x/YJ47 which recommends pretty much the code you showed. Alan Hoenig's TeX Unbound: LaTeX & TeX Strategies for Fonts, Graphics, & More shows a similar definition on p. 546. The definition is quite similar in style to the one in apalike.sty. I also found several LaTeX 2.09 .stys with similar idioms using enumi (http://mirrors.ctan.org/macros/latex209/contrib/misc/chapref.sty, http://mirrors.ctan.org/macros/latex209/contrib/misc/cites.sty). Maybe the code is inspired by older LaTeX 2.09 code?