How to get really big curly braces

Just use \left\{ and \right\} for the braces as well:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

Original equation:
\begin{equation*}
  \pi(X) = \mathbf{N}_4 \Bigg\{ \left(
  \begin{matrix}
    1 \\ 2 \\ 1 \\ 3
  \end{matrix}
  \right), \left(
  \begin{matrix}
    2 & 1 & 2 & 3 \\
    1 & 2 & 1 & 3 \\
    2 & 1 & 3 & 3 \\
    3 & 3 & 3 & 7
  \end{matrix}
  \right) \Bigg\}
\end{equation*}

Updated equation:
\begin{equation*}
  \pi(X) = \mathbf{N}_4 \left\{ \left(
  \begin{matrix}
    1 \\ 2 \\ 1 \\ 3
  \end{matrix}
  \right), \left(
  \begin{matrix}
    2 & 1 & 2 & 3 \\
    1 & 2 & 1 & 3 \\
    2 & 1 & 3 & 3 \\
    3 & 3 & 3 & 7
  \end{matrix}
  \right) \right\}
\end{equation*}

\end{document}

This is one of the few situations that warrants the usage of \left and \right for automatically sized delimiters. If you want to manually size your delimiters at any cost you can easily define more sizes. Therefore I made the factory \makebig. It takes a name and a size and defines the corresponding macros and the open and close variants.

For the braced matrices you can just use pmatrix from the amsmath package.

EDIT: amsmath has a smarter mechanism to define new manually sized delimiters. Thanks for pointing it out egreg.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\newcommand\makebig[2]{%
  \@xp\newcommand\@xp*\csname#1\endcsname{\bBigg@{#2}}%
  \@xp\newcommand\@xp*\csname#1l\endcsname{\@xp\mathopen\csname#1\endcsname}%
  \@xp\newcommand\@xp*\csname#1r\endcsname{\@xp\mathclose\csname#1\endcsname}%
}
\makeatother

\makebig{biggg} {3.0}
\makebig{Biggg} {3.5}
\makebig{bigggg}{4.0}
\makebig{Bigggg}{4.5}

\begin{document}
\begin{equation*}
  \pi(X) = \mathbf{N}_4 \biggggl\{
  \begin{pmatrix}
    1 \\ 2 \\ 1 \\ 3
  \end{pmatrix},
  \begin{pmatrix}
      2 & 1 & 2 & 3 \\
      1 & 2 & 1 & 3 \\
      2 & 1 & 3 & 3 \\
      3 & 3 & 3 & 7 \\
    \end{pmatrix}
  \biggggr\}
\end{equation*}
\end{document}