Unit column in table with square brackets and siunitx

1. Please unlearn your habit of using \left ... \right all over

2. Drop the [], they do nothing to the interpretation of that column

3. use the s column, and in that column just write say \meter

In code

\documentclass[10pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{siunitx}
\usepackage{array,booktabs}
\newcolumntype{M}{>{$} c <{$}}
\newcommand\mc[1]{\multicolumn{1}{c}{#1}}
\begin{document}

\begin{tabular}{M l s } %|
\toprule
\mc{Variable} & Meaning & \mc{Unit} \\
\midrule
R & Radius for BNBO & \meter\\
Q & Extraction rate & \cubic\meter\per\second\\
t & Time frame for BNBO & \second\\
b & Aquifer thickness & \meter\\
n_{\textup{eff}} & Effective porosity & \mc{---} \\
\bottomrule
\end{tabular}
\end{document}

This can be done with the help of the collcell package (loads array).

Just define your column as

\newcolumntype{U}{>{$[\collectcell\si} l <{\endcollectcell]$}}

and you're done.

MWE

\documentclass[10pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{siunitx}
\usepackage{collcell} % loads array
    \newcolumntype{M}{>{$} l <{$}}
    \newcolumntype{U}{>{$[\collectcell\si} l <{\endcollectcell]$}}

\begin{document}

\begin{equation}
R = \sqrt{Q\: \frac{t}{\pi\: b\: n_{eff}}}
\end{equation}

Where:\bigskip

\begin{tabular}{M |l U}
    R & Radius for BNBO & \meter\\
    Q & Extraction rate & \cubic\meter\per\second\\
    t & Time frame for BNBO & \second\\
    b & Aquifer thickness & \meter\\
    n_{\textit{eff}} & Effective porosity & -\\
\end{tabular}
\end{document}

Output

Notice that the right way to add some spacing is not \\ but something like \bigskip. Also, usign align when there is nothing to align is not the best choice, use equation instead.

If you really want, but I would avoid it, you can even add \left and \right

\newcolumntype{U}{>{$\left[\collectcell\si} l <{\endcollectcell\right]$}}

You add no meaning with the units in brackets; in my opinion it's even wrong, as usually brackets denote abstract dimensions, such as “length·time^–1” or “force·length”.

The s column type is what you're looking for. I also removed all \: spacing commands, which are wrong, and set “eff” in upright type.

Note also that Where:\bigskip would allow a page break after it.

\documentclass[10pt,a4paper]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{siunitx}

\newcolumntype{M}{>{$} l <{$}}
\newcommand{\eff}{\textrm{eff}}

\begin{document}

\begin{equation}
R = \sqrt{Q \frac{t}{\pi b n_{\eff}}}
\end{equation}
Where:\\*[\bigskipamount]
\begin{tabular}{M l s}
R & Radius for BNBO & \meter\\
Q & Extraction rate & \cubic\meter\per\second\\
t & Time frame for BNBO & \second\\
b & Aquifer thickness & \meter\\
n_{\eff} & Effective porosity & \multicolumn{1}{c}{--}\\
\end{tabular}
\end{document}