Q:

What does the prefix "\c@" mean in build log?

I just follow the LaTeX tutorial to create the first "Hello World!" .tex file, and translate it to PDF file.
Then I go through the .log file and see the following,
("C:\Program Files\MikTeX\tex\latex\base\size10.clo"
File: size10.clo 2014/09/29 v1.4h Standard LaTeX file (size option)
)
\c@part=\count79
\c@section=\count80
\c@subsection=\count81
\c@subsubsection=\count82
\c@paragraph=\count83
\c@subparagraph=\count84
\c@figure=\count85
\c@table=\count86
\abovecaptionskip=\skip41
\belowcaptionskip=\skip42
\bibindent=\dimen102
) (hello_world.aux)

I am confused with the statements, like
\c@part=\count79

Anyone can explain this?

A:

You probably compiled the following minimal example:
\documentclass{article}
\begin{document}
Hello World!
\end{document}

which provided the following (partial) .log:
...
\c@part=\count79
\c@section=\count80
\c@subsection=\count81
\c@subsubsection=\count82
\c@paragraph=\count83
\c@subparagraph=\count84
\c@figure=\count85
\c@table=\count86
...

The above output stems from counter definitions within the default article document class. More specifically, the following set of commands (just search for \newcounter in article.cls):
...
\newcounter {part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]
...
\newcounter{figure}
...
\newcounter{table}
...

Each \newcounter{<newcntr>}[<oldcntr>] defines a new counter as a macro \c@<newcntr> - note the prefix c@. Here's the definition of \newcounter from the LaTeX kernel:
\def\newcounter#1{%
  \expandafter\@ifdefinable \csname c@#1\endcsname
    {\@definecounter{#1}}%
  \@ifnextchar[{\@newctr{#1}}{}}

At first it checks whether a macro \c@<newcntr> already exists, and then defines it via \@definecounter{<newcntr>}.
\def\@definecounter#1{\expandafter\newcount\csname c@#1\endcsname
  ...}

\@definecounter issues the TeX primitive \newcount to create the actual count register that \c@<newcntr> points to.
The use of the c@ prefix is purely a conventional choice. In a similar manner, counter prefixes have a p@ macro prefix, while references (or \labels) in the LaTeX kernel have an r@ prefix. It attempts to avoid end-users from messing around with the counters, yet still allow them to create their own similarly-named macros. That is, making the following work without problem:
\newcounter{something}% <------- Creates \c@something
\newcommand{\something}{..}% <-- Creates \something

If the c@ prefix wasn't inserted by \newcounter, then \newcounter{something} may very well have created a counter macro \something, which is problematic when you want to create a real macro \something.

