Problem formatting a subscript in math mode

You may want to load the amsmath package to access its \text macro and type (in math mode, obviously):

\nu_{\text{FWHM}}

Don't use the \rm command in a LaTeX document.

Addendum -- @AndrewSwann has pointed out that FHWM, being an acronym, should be typeset in small-caps letters, i.e., as \textsc{fhwm}. Defining the acronym command \FHWM with \newcommand\FHWM{\textsc{fhwm}}, the following possibilities arise for typesetting the acronym as a subscript to \nu:

$\nu_{\text{FWHM}}$ % regular caps, subscript in "scriptsize" font size

$\nu_\FHWM$         % small caps, subscript in "scriptsize" font size

$\nu_{\text{\tiny\FHWM}} $  %  small caps, subscript in "tiny" font size

This will overlap with Mico's answer, but there are couple of extra points that I'd like to make.

Loading amsmath has the nice feature that text font changing commands may be used in mathematics and the text resizes appropriately in subscripts etc. The commands \textrm, \textit etc. may be used directly without having to invoke an additional \text command. Often these direct commands are to be preferred over \text, because the latter inherits the font characterisitics from the surounding text. My standard solution for such situation is to define a macro and use the \textnormal command to avoid this.

\documentclass{article}

\usepackage{amsmath,amsthm}

\newtheorem{theorem}{Theorem}

\newcommand{\FHWM}{\textnormal{FHWM}}

\begin{document}

\( B_\FHWM \) vs. \( B_{\text{FHWM}} \) and
\( X_{B_\FHWM} \) vs. \( X_{B_{\text{FHWM}}} \)

\begin{theorem}
 Preferring \( B_\FHWM \) to  \( B_{\text{FHWM}} \)
\end{theorem}

\textbf{\( B_\FHWM \) vs. \( B_{\text{FHWM}} \)}
\end{document}

An alternative to \textnormal is \textup, which will produce upright inside italic and slanted text, but will turn bold inside bold text.

However, in your case you are putting the subscript on a small symbol \nu and the above looks too big. The small caps shape from \textsc is often designed to give the best spacing for such combinations and is a standard choice for acronyms. You need to remember to write \textsc{fwhm} instead of \textsc{FWHM} as the latter usually produces capitals of the same size as \textrm capitals. One thing to be aware of is that the standard fonts have no bold variant of \textsc, so I suggest you additionally use \textnormal to avoid surprises. Your request for a very small font is provided by the \tiny command. (My personal preference would be to omit that or to use a command from the relsize package.) Below is an example with \tiny included.

\documentclass{article}

\usepackage{amsmath,amsthm}

\newtheorem{theorem}{Theorem}

\newcommand{\FHWM}{\textnormal{\tiny \textsc{fhwm}}}

\begin{document}

\( \nu_\FHWM \) vs. \( \nu_{\textsc{fhwm}} \) vs. \( \nu_{\text{FHWM}} \) 
and
\( X_{\nu_\FHWM} \) vs. \( X_{\nu_{\textsc{fhwm}}} \) vs. \( X_{\nu_{\text{FHWM}}} \)

\begin{theorem}
 Preferring \( \nu_\FHWM \) to  \( \nu_{\text{FHWM}} \)
\end{theorem}

\textbf{\( \nu_\FHWM \) vs. \( \nu_{\textsc{fhwm}} \) vs. \( \nu_{\text{FHWM}} \)}
\end{document}

The bold cases in the above examples are there just to illustrate pitfalls. If you really intend to use this in such contexts, then you need to think about what fonts you wish to appear and build the commands appropriately.