In law, we are taught, "make it fresh and vivid." Stories do that when they are well told. People relate. It makes an abstraction real to them by bringing their experience into play. It gives them a hook by which to remember an important point. This does not mean, "tell a story every time you want to make a point" because straining for effect while trying to persuade, even in trying to weave stories into your narrative, is self-defeating. The point is not to show how how clever or artful you are, it is to make your points in ways that will stick. To do that, you need above all to be sincere and credible. You need to use the power of logic where it applies. You need to bring in emotive elements when apt and when they fit naturally into your narrative. You need to use imagery that is original, not borrowed, drawing from your experience if possible and then from the use of a vigorous imagination. And you need to do all this with forceful use of language, with active style that moves quickly without pausing to try to impress.

When you do all that, and do it well, you will find your audience at each level relating to you and to what you are saying. Stories can add powerfully to that relational effect. Like a fellow out in nature watching birds from afar and suddenly seeing them up close and vividly through magnification, your hearer or reader will find himself drawn close to what might otherwise be a distant narrative through stories that enliven the very things he is eager to see. Your audience wants to relate. Help them along with this with stories where apt. If knowing the science behind this helps, apply that as well. But, at least as far as effective communication goes, don't forget the broader context. We get bored and glaze over all too easily. Make it fresh and vivid. Make it original. Make it memorable. Then you will have spoken or written well. And your audience will value what you give them.