To hang wash yoru clothes is similar to hang drying them, only more lazy. It constitutes putting worn clothes on a hanger or over a shower curtain or towel rack for a few days. After an appropriate amount of time, the clothes are considered "clean" again.
There may be a limit imposed on how many times clothes can be hang washed before they must be subjected to actual soap and water.
Dude 1: When the washer in my apartment broke, I had to hang wash my clothes for an entire month!
Dude 2: Dude 1, that's gross.