The formal definition of an introduction is a brief introductory passage. What is important is that you get the story right. It should encapsulate the essence or spirit of your overall point and communicate that point through examples. 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 write, 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. Ask yourself; is it short enough that a reader will not lose his or her 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 if 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 for within the story.
Starting with a long introduction that bears no relevance to the headline is the number one killer of otherwise good writing. When using long anecdotes, let readers know before you begin how it relates to your topic, or many readers will drop out of your article before you 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 and consider which details help do this and which do not. Extra details like dates, names, descriptions, and diversions, if unnecessary to the essence of the anecdote, serve only to distract the reader.