Rubbish is an item produced when items decay over time. It quickly decays unless placed in a very cold area or on a Display. To obtain Rubbish, place Food or other Items that decay quickly (such as Amber Fruit) in a hot room and wait for them to decay.
It is useless in most cases, however Sect Leaders often have it as a Liked Item, allowing one to gain Sect Favor and Connection by gifting Rubbish to the Sect Leader.