A hagoromo (羽衣, lit. "Feather Robe") is a long, thin shawl often associated with far-east celestial beings and deities.
Despite being thin, it is often depicted being able to remain upright in the air on its own. The cloth was modeled after ancient China's clothing called, pi-bo (披帛).
Tales associated with the hagoromo include the Japanese legend of tennin (spirtual beings who wear hagoromo) and some folkloric stories set in China, for example, Orihime and Hikoboshi.
Buddhist deities' hagoromo-like shawls are called "天衣" (Chinese: tian yi, Japanese: tenne, ten'e, or ten'i). On Danbooru, tian yi should be tagged as hagoromo for convenience.
This tag implicates shawl (learn more).