Accordion in Joomla context is a way to display Joomla content items in an accordion-like way. You or your site visitor clicks on an item. In response, another item slides down underneath of the first item.
Please check out the "Sliders example" on Tabs & Sliders demo page to see accordion in action.
You basically have one content item being on display and another, linked to it, hidden. Such design can be useful to compactly arrange a fairly small amount of content items on a limited screen estate.
You most commonly find accordeon-like design applied to FAQ sections.