Right click the images to see them full size.
This is more data art than infographic. The kinda vagueness of the graphic representation of information is a deliberate choice, but each ring represents a year since 1903, (the first World Series season, apart from expansion teams which begin at their first seasons), from the centre outwards. The colours are, obviously, of the specific teams. Grey rings represent seasons without any postseason success. The darker the colour represents a level of postseason play. World Series victories are usually represented in a different colour. Yankees and White Sox don't follow this, they just have the darkest level of the main colour use.

Prints of all of these are available at Society6

And here's an extra one featuring the three teams in Washington, D.C. over the years.