To get the "displaystyle", i.e., large, fractional expressions to the right of the curly brace, either use \dfrac instead of \frac or employ the dcases environment (requires the mathtools package) instead of the "basic" cases environment. As the other comments and answers have already noted, used \boxed to enclose the equation in a rectangular frame.
By the way, the \text{$...$} wrappers are unnecessary; just write out the argument.

\documentclass{article}
\usepackage{mathtools} % for 'dcases' environment
\begin{document}
\begin{equation}
\boxed{
\sigma_{\mathrm{ann}} \propto
\begin{dcases}
\frac{\lambda_3^2 m_b^2}{m_H^4} & m_S\ll\frac{m_H}{2}\\[1ex]
\frac{\lambda_3^2 m_b^2}{m_H^2\Gamma_H^2} & m_S=\frac{m_H}{2}\\[1ex]
\frac{\lambda_3^2 m_b^2}{m_H^2\Gamma_H^2} & m_S=\frac{m_H}{2}
\end{dcases}
}
\end{equation}
\end{document}
\begin{equation} \boxed{...} \end{equation}– touhami May 19 '16 at 20:08