Accordions (at least web versions) generally only have one section open at a time…See Jquerys version. (http://jqueryui.com/accordion/)
Otherwise, it’s something else (technically) but I get your question.
For myself, I prefer to have multiple content sections open, so I can refer back without having to close where I am and re-open another section.
However, what the final functionality should be will, I suspect, depend on what the content is intended to be and what you want the user to do.