Typically we tend to tell stories in chronological order. “First this happened, then this happened and then this other thing happened.”
They’ll start with a scene, often the most exciting or emotionally engaging scene they can. Then after they play out that dramatic scene, they flash back in time to the beginning of the story and fill the listener in on what led up to that point.
Starting in the middle of the story has a couple of advantages, Firstly, if you start with the most dramatic part of the story you can grab your audience and really get them emotionally invested in the story right off the bat. The second advantage is that you’re giving the audience a bit of variety. If you’re doing a long talk, or if you’re one of a number of speakers that day, people are probably going to hear more than one story from the stage. So if you can change up how you tell the story it keeps you from sounding just like everyone else.
Starting a story from the middle and doing the time travel routine is like adding a hot spice to a meal – use it sparingly. If you start telling all of your stories this way the novelty will wear off quickly and your talk will be harder for the audience to follow.