Known as the Land of Myth, Izumo has many myths recorded in the earliest chronicles, and probably the most well known is the story of Susano slaying the Yamata no Orochi, a fearsome dragon with 8 heads and 8 tails.
There are many different explanations of what exactly this great serpent was, but the most common one is that it refers to the 8 tributaries that drain the Okuizumo area and combine to form the Hi River.
The route of the Izumo 33 Kannon Pilgrimage passes through the watershed of the Hi River for about 100k, so its not surprising that the towns in the area incorporate the Orochi in their manhole designs.
The first one I found near Hinobori, The second In Kisuki also features the local bridge. The third from Mitoya includes Susano and the princess Inada who he saves from the Orochi. The fourth, from Yokota is in the heart of the myth country. Near here is where Inada and her family lived. The final photo is the main design found in Izumo City itself.