I'd second what TechieGuy says: I found the site quite difficult to use, and incredibly slow on my (admittedly quite old) laptop.
But basically what you're after is an accordion menu. Google has plenty of examples with code. There's a
plug and play one that's part of the jQuery UI, though it doesn't look like it has an option to expand horizontally.
Here's another jQuery example that should be easy to adapt to work horizontally: essentially you need to replace the slideUp and slideDown with custom
animate calls (to animate the ul width) and you're done, barring the CSS work of course.