You'll most likely find the significance a lot more understandable, what with Wyoming's huge ranching industry, not to mention its place in the history of the Wild, Wild West. We passed through town recently, and the boots are one thing that jumped out at me. Although I didn't have time to search out all of them, I did get photos of a few that are at the Depot Square. The boots are well over my 5'5" height, and each is colorful, and different.
There are 18 of these 8-ft. tall boots throughout the Cheyenne area, five of them at the Cheyenne Depot Square (two of them are shown here). They were part of a 2004 public art fundraising campaign, and if you want to do a boot scavenger hunt and look for all of them, you can pick up a map at the museum.