If your use case doesn't require you to create cross-references to the "units", @Dr.ManuelKuehner's simple and straightforward answer is perfectly adequate.
In, however, if you foresee a need to create cross-references of the units, it's better not to incorporate the word "Unit" directly into the macro \thesubsection
. Instead, it would be better to make use of the low-level LaTeX command \@seccntformat
; see below for an implementation of this idea. If you pursue this approach, as an added bonus you can make use of the cross-referencing capabilities of the cleveref
package, e.g., use a \cref
or \Cref
command to create a cross-referencing call-out to multiple objects in one go.
Incidentally, the \@seccntformat
approach works equally well with the Koma-Script document classes and with the "basic" LaTeX document classes (article
, report
and book
).

\documentclass{scrartcl}
% Method proposed in "The LaTeX Companion", 2nd ed.:
\makeatletter
\def\@seccntformat#1{\@ifundefined{#1@cntformat}%
{\csname the#1\endcsname\space}% default
{\csname #1@cntformat\endcsname}}% enable individual control
\newcommand\subsection@cntformat{Unit \thesubsection\@.\space} % subsection level
\makeatother
\renewcommand\thesubsection{\Roman{subsection}}
\usepackage{cleveref} % for \cref and \Cref macros
\crefname{subsection}{unit}{units} % label to be used in cross-references
\begin{document}
\section{Hello} \label{sec:hello}
\subsection{World} \label{sec:world}
\subsection{Solar System} \label{sec:system}
\subsection{Galaxy} \label{sec:galaxy}
\subsection{Universe} \label{sec:universe}
As required, the first subsection header says \textbf{Unit I\@. World}.
\medskip
\noindent
As shown in \Cref{sec:world,sec:galaxy,sec:universe} of \Cref{sec:hello}, \dots
\end{document}