Cooper Thomas from ESRI's StoryMaps team created a very nice Add a swipe block to your story tutorial. The video tutorials below demonstrate creating a swipe map with the Village of Dearborn (1891) on the left compared to the City of Dearborn (1947) on the right.
You don't have to have maps to use this feature! You can use photographs, too. For example, you can have a historic photo of a building on the left and a current photo of the same building on the right. Then, you can swipe to compare the images to see what has changed.