The formal definition of an intro is a brief introductory passage. What is important is that you get the story right; it needs to encapsulate the essence or spirit of your overall point, try communicating through example. Capturing the essence is not enough; if nobody reads far enough to grasp the main point of the story then its purpose is lost.
If you are going to start writing, make sure it is a short intro. When readers see a headline they expect the writing below it to contain content which relates to that headline. There is only so much time a reader will spend with an intro about sports when the headline suggested the article was about vacations. Even if the intro, at its end, would have captured the essence of what the author was trying to say. Ask yourself; is it short enough that a reader is not losing his patience before the writing returns to the topic at hand?
The piece above contains an intro that is quite short. This kind of intro has the potential to work very well as long as the reader knows what they are reading. Readers know what the article is going to tell them in broad terms and so they know what to look-out for within the story.
Starting with a long introduction that appears to bear no relevance to the headline is the number one killer of otherwise good writing. When using long anecdotes you need to let your readers know before you begin how it relates to your topic, or many readers will drop out of your article before you have a chance to illustrate your point.
More essence in fewer words; the function of an introduction is to convey something about your broader point. Think about your intro as a whole and consider which details help do this and which do not. Extra details like dates, names, descriptions and diversions, if not necessary to the essence of the anecdote, serve only to distract the reader.