One option would be to use the fancytooltips package. A little example follows:
First, you create the PDF file containing the tooltips (one per page). You can do this using latex; for your example, I used the following practice.tex document (mdframed was used to present the tooltips using a nice colored framed box with a shadow, but of course you can decorate the tooltips as you wish):
\documentclass{article}
\usepackage[rmargin=11cm]{geometry}
\usepackage{amsmath,amssymb,mathtools}
\usepackage[createtips]{fancytooltips}
\usepackage{xcolor}
\usepackage[framemethod=TikZ,shadow]{mdframed}
\usetikzlibrary{shadows}
\newmdenv[linecolor=olive,backgroundcolor=yellow!10,shadow=true]{infobox}
\begin{document}
\keytip{character}
\begin{infobox}
Let $\sigma\colon G\to \mathsf{GL}(\mathbb{C}^{n})$ be a representation of a group $G$. The character of $\sigma$ to be the function $\chi_{\sigma}\colon G\to \mathbb{C}$ by $\chi_{\sigma}(x):=\mathrm{Tr}\sigma(x)$.
\end{infobox}
\newpage
\end{document}
This document has to be processed to obtain practice.pdf. Now you create your main document (notice that the name used in filename= is precisely the name of the file practice.pdf containig the tooltips):
\documentclass{article}
\usepackage{xcolor}
\usepackage[filename=practice]{fancytooltips}
\begin{document}
\tooltip*{Definition: Character of a Group Representation}{character}
\end{document}
In the main document, the tooltips will now be invisible until you click on the little blue ballon.
An image of the obtained document without uncovering the tooltip:

And now an image of the obtained document with the tooltip:

This approach doesn't work in all PDF viewers, since it requires cooperation with JavaScripts; you have to use Adobe Reader or Adobe Acrobat to see the tooltips.
hyperref. Specifically, read section 6 PDF and HTML forms. – Werner Apr 18 '12 at 19:39