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