When using a Rest Stop, one of the options is to Clean Clothes. The description on it is "Clean all your equipment". What does that actually do, though?
Nothing, it's just aesthetic.
While out adventuring in the lands of Aionios, your party's character models will slowly start accumulating dust and grime. Cleaning their clothes at a Rest Spot gets rid of the dirt, giving your party members clean clothes before resuming travel.
Do note, this feature is entirely for immersion purposes. Whether clean or grimy, the story and gameplay of Xenoblade Chronicles 3 will not be directly affected by this mechanic.
According to Game8.