What does \z@ do?

latex.ltx says

\newdimen\z@ \z@=0pt % can be used both for 0pt and 0

so as it says it is short (and efficient) way of getting 0.

You should always have a copy of the latex source file latex.ltx in a text editor window while reading package code:-), or perhaps, if you prefer, the typeset version of that, without the comments being removed, source2e.pdf, this is available in most distributions, or may be typeset from the sources.

Note that \count@=\z@ is more efficient than \count@=0 as \z@ is a register so terminates the scan for a number. But 0 might be the first token in 0123 so TeX has to read ahead to find the next token, if it is a space, discard it, if it is anything else it needs to put the token back into its input stream to be read after the assignment.

---

A Test file:

\catcode`@=11
%\def\a{\dimen@=\z@}
\def\a{\dimen@=0pt\relax}
\def\b{\a\a\a\a\a\a\a\a\a\a}
\def\c{\b\b\b\b\b\b\b\b\b\b}
\def\d{\c\c\c\c\c\c\c\c\c\c}
\def\e{\d\d\d\d\d\d\d\d\d\d}
\def\f{\e\e\e\e\e\e\e\e\e\e}
\def\g{\f\f\f\f\f\f\f\f\f\f}
\def\h{\g\g\g\g\g\g\g\g\g\g}

\h

\bye

Doing a few runs of each two and taking a typical timing, with 0pt as above:

$ time tex zat
This is TeX, Version 3.1415926 (TeX Live 2011/Cygwin)
(./zat.tex )
No pages of output.
Transcript written on zat.log.

real    0m3.822s
user    0m3.774s
sys     0m0.015s

With the % moved a line so it uses \z@:

$ time tex zat
This is TeX, Version 3.1415926 (TeX Live 2011/Cygwin)
(./zat.tex )
No pages of output.
Transcript written on zat.log.

real    0m1.080s
user    0m1.029s
sys     0m0.030s

This is an easily observable difference, even without using the time command. 10^7 is quite a few assignments but probably not impossibly many.

\z@ is a LaTeX “constant” that's defined to be zero. Package developers can use it to assign or test against the value 0 and it can also replace a length of 0pt. Similar constants are \@ne (one) \tw@ (two) and so on. Due to the @ they can only be used in packages or between \makeatletter and \makeatother.