Like obscenity, I'll know it when I hear it.

OK.  That's completely unhelpful, isn't it?

I can tell you things to avoid, if that helps.

Avoid being the hero or the victim of your story.  The audience isn't there to be your fucking therapist or the witness to your bragging.
Avoid stories that include a lot of "...and THEN..." because that's how a five-year old tells a story.
Avoid trying to make us laugh.  That's stand up.  And do NOT laugh at your own jokes (if you ignore that part about not trying to be funny...)

DO
Start with a killer sentence that makes me want to know what happens next.
End with a moment that indicates your transformation.
Fill in the rest with colorful, rich details as well as action.

What makes a great story?  It takes into account the following:

People want to be liked.

We all crave attention and affection and we all reject shame. When we get embarrassed we send a thug version of ourselves to the forefront to do our fighting for us. We’re at the top of the food chain just under fear. We don’t want to be in a relationship to hear the words “I love you”, we want to be in a relationship to say the words “I love you”.

We want to feel needed, and exceptional and we hate feeling insignificant. We want to ace a hearing test. We are binary creatures, if we’re the plaintiff, we want to win every dollar. If we’re the defendant, we want to guard every penny. We want to make more money than last year. We don’t want to get cancer or die in our cars and we want the same for our loved ones.

We go out on weekends to try and have sex while trying not to get punched in the face. We drink so we can be ourselves and not mind it so much. We’re desperate to be understood. We want to know someone else has felt it, too.

We hate being judged unfairly. We want to make the person we heard wasn’t all that into us change their minds and admit they had us wrong. We want sunny skies with a chance of killer tornadoes, just to keep the music sounding good. We take hours upon hours to admit to self consciousness. We don’t know exactly how to please each other.

We just want love. In any and every form. — John Mayer

Now go try.  And fail.  And try some more.  And fail some more.  But never stop telling your stories because stories are the essence of what makes us human.