Curly braces and nested arrays
You have a typo in your inner array
change
\begin{array}{1}
%%%
to
\begin{array}{l}
%%%
To give you another possibility using cases
from amsmath
or mathtools
.
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
DTW(A,B)=\begin{cases}
0 \quad \phantom{\infty}\text{if}\,\, n=0 \,\,\text{and}\,\, m=0 \\
\infty \quad \phantom{0} \text{if}\,\, n=0 \,\,\text{and}\,\, m=0 \\
{d(H(A),H(B))+\min \begin{cases}
a\\
b\\
c\\
\end{cases}}
\end{cases}
\end{equation}
\end{document}