How to get this dot in the picture?

R. Schumacher already answered what the symbol means. How to get it with LaTeX is a different question. Here are five different versions all of which don't look perfect in the default settings:
\documentclass{article}
\usepackage{chemformula,mhchem,array}
\newcommand*\cs[1]{\texttt{\textbackslash#1}}
\begin{document}
\newcounter{version}
\setlength\extrarowheight{2pt}
\begin{tabular}{>{\stepcounter{version}\theversion.\quad}ll}
. & $\mathrm{O}_2^{.-}$ \\
\cs{cdot} & $\mathrm{O}_2^{\cdot-}$ \\
\cs{bullet} & $\mathrm{O}_2^{\bullet-}$ \\
mhchem & \ce{O2^{.-}} \\
chemformula & \ch{O2^{.-}} \\
\end{tabular}
\end{document}

To me version 3. clearly is much too big to look good and not an option. Versions 1. and 2. are arguably too small although \cdot doesn't look too bad in my opinion. In the mhchem version the dot and the minus sign are very close while in the chemformula version they're not perfectly aligned. I prefer the chemformula version nonetheless because it is adjustable:
\documentclass{article}
\usepackage{chemformula}
\begin{document}
\ch{O2^{.-}}
\setchemformula{radical-radius=1pt}
\ch{O2^{.-}}
\setchemformula{
radical-radius=.5pt ,
radical-vshift=.444ex
}
\ch{O2^{.-}}
\end{document}

That symbol when used in Chemistry (usually with the full bonds between atoms) denotes an extra free electron (it negative charge). The minus is actually saying it twice.
These are usually used in Lewis Dot Structures (Diagrams) and mean a free electron (unbonded). Lewis Structure
Or when you see this you are describing an Oxygen radical (ie negative charge).
Also this entire area of notation is very much author and sub discipline dependent, so you need to verify exactly what the author/discipline in meaning in that context.
And as the preceding offered you would just use \bullet.
While there's arguably a degree of tautology (some might say 'precision') in writing $\ce{O2^{.-}}$ -- as an $\ce{O2}$ radical will always have a negative charge, and a negatively charged $\ce{O2}$ will always be a radical -- the two things are by no means synonymous. In other species, for instance atomic oxygen, a lone oxygen atom, $\ce{O^{.}}$ has no charge, while an oxygen ion, $\ce{O-}$ is not a radical.
– owjburnham Sep 20 '17 at 14:22