Undefined control sequence when using \edef with \foreach

I had to speculate what you want to do, so my guess it is something like this:

\documentclass[11pt,a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\usepackage{xparse}
\usepackage{etoolbox}
\usepackage{siunitx}
\tikzset{ht_num/.style={draw, semithick},
ht_hash/.style={draw, semithick, minimum width=2em}}
\begin{document}

\NewDocumentCommand \HashTable { m m } {%
    \def\MatrixContent{\empty}
    \pgfmathtruncatemacro\nn{2^#2-1}
    \foreach \n in {0,...,\nn}{%
        \pgfmathbin{\n}%
        \edef\myresult{|[ht_hash]| 
        \num[minimum-integer-digits=#2]{\pgfmathresult}}%
        \xappto\MatrixContent{\expandonce{\myresult\\}}%
    }
    \matrix [outer sep=0pt,matrix of nodes] (#1) {
        |[ht_num,name=#1-a]|  #2 \\
        \MatrixContent %\\
    };
}

\begin{tikzpicture}
    \HashTable{table1}{2}
\end{tikzpicture}
\end{document}

Comments:

1. You were loading but not using the matrix library. I think using it makes things much simpler here.
2. \tikzstyle is deprecated.
3. I basically used the commented out solution in Martin Scharrer's answer.
4. A TikZ matrix has counts \pgfmatrixcurrentrow and \pgfmatrixcurrentcolumn which, when used, may allow you to make this whole enterprise much simpler. Yet I am not sure I am on the right track.

There are several problems in your code.

1. \foreach executes each cycle in a group, so any definition made inside it is forgotten as soon as the group ends, unless it is done globally; thus not \edef, but \xdef (global expanded definition)

2. The code \unexpanded\expandafter{\MatrixContent} is meant to access the previous value of \MatrixContents (but with no further expansion). You don't want to expand \node..., so that should be the argument of a simple \unexpanded; however it is the only token that should be protected from expansion, together with \\, so a couple of \noexpand suffice; \num is by itself protected from expanding in \edef or \xdef.

3. Further problem: \num wants to see a number, not the set of instruction to produce it, so \pgfmathbin{\n} should be done before updating \MatrixContent; and \pgfmathresult should not be hidden in \unexpanded.

4. \tikzstyle has been deprecated for a few years.

Here's the amended code:

\documentclass{article}

\usepackage{siunitx}
\usepackage{tikz}

\begin{document}

\tikzset{
  ht_num/.style={draw, semithick},
  ht_hash/.style={draw, semithick, minimum width=2em},
}

\newcommand\HashTable[2]{%
  \def\MatrixContent{}% not \empty
  \pgfmathtruncatemacro\nn{2^(#2)-1}
  \foreach \n in {0,...,\nn}{%
    \pgfmathbin{\n}% the current value in binary format
    \xdef\MatrixContent{%
      \unexpanded\expandafter{\MatrixContent}% the previous value
      \noexpand\node[ht_hash] (#1-\n) {\num[minimum-integer-digits=#2]{\pgfmathresult}};
      \noexpand\\%
    }%
  }%
  \matrix [outer sep=0pt,every node/.style={anchor=west}] (#1) {
        \node[ht_num] (#1-a) {#2}; \\
        \MatrixContent
  };
}

\begin{tikzpicture}
    \HashTable{table1}{2}
    % Other tikz nodes...
\end{tikzpicture}
\qquad
\begin{tikzpicture}
    \HashTable{table1}{3}
    % Other tikz nodes...
\end{tikzpicture}

\end{document}