A story has to grab the attention of your audience.
It should be something your audience can in some way identify with.
It should have a point to it. A beginning, a middle, and an end are improtant to have.
::Advice::
Take acting classes.
Listen to other good story tellers, and identify what it is about them that makes them good. You can look anywhere from books to movies and everything in between.
Now a story is important to me, since I graduated with an animation degree. I also perform magic, where it is very important to hook the audience with a good story. My favorite illusions involve stories.
An example:
I own an effect where a person picks a card out of a deck. I show 4 extra cards, all with little aliens on them. The alien cards change, and then I end up with 4 copies of the card they chose. Then they change back, and I'm done.
That sounds boring.
Now if you add a story about how this astronomer in deckville has first contact, meets these aliens, they probe him and then take his form. He devises a plan for escaping the ship, and he succeeds. The aliens leave, saddened that their mission was a failure... well, it adds something more to the idea of cards changing. It has a point to it, and it holds a little bit of interest, since you do kind of get (A little bit) attached to the character of the astronomer. It has a beginning, a middle and an end, and the hero wins.
Story is very important. It's something to always be looked at.
I hope this helped. Good luck.