While blank lines are not illegal in an array environment, generally, they are inside the display environments defined by amsmath such as align or gather. Also empheq doesn't accept them.
In these cases the blank lines are caught before array can deal with them.
The solution is
never use blank lines in math mode.
Here I made up definitions for \ii, \jj and \kk and also copied one for \mybox from an example in the site. In future questions, please provide these details and make your example codes compilable.
I also used vmatrix instead of array, because it makes for better spacing.
\documentclass{article}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{empheq}
\usepackage[many]{tcolorbox}
\newcommand{\ii}{\vec{\imath}}
\newcommand{\jj}{\vec{\jmath}}
\newcommand{\kk}{\vec{k}}
\newtcbox{\mymath}[1][]{
nobeforeafter,
math upper,
tcbox raise base,
enhanced,
boxrule=1pt,
drop lifted shadow,
sharp corners,
#1,
}
\begin{document}
\begin{empheq}[box={\mymath[colback=Bittersweet!20]}]{equation}
\vec{a}\times \vec{b}=
\begin{vmatrix}
\ii & \jj & \kk \\
a_x & a_y & a_z \\
b_x & b_y & b_z \\
\end{vmatrix}
\end{empheq}
\end{document}

\ii,\jj,\kk,\vecand\mymathare not defined. I think the empty lines inside thearrayare likely the problem though. – Circumscribe Nov 10 '18 at 09:29arrayconstruction with\begin{vmatrix} ... \end{vmatrix}, defined byamsmath(whichempheqloads). – Bernard Nov 10 '18 at 10:20