。
She wanted to wash the dirty kimono.
Literal
She [topic-は] became-dirty kimono [object-を] wash wanted.
汚れた is the past form of 汚れる ('to become dirty') used as an attributive — Japanese commonly uses past forms before nouns to express a resulting state, so 汚れた着物 reads as 'a kimono that has become dirty' = 'a dirty kimono.' This past-as-modifier construction is everywhere: 疲れた顔 ('tired face'), 古びた家 ('aged house'). The desiderative ~たい conjugates like an い-adjective, so its past form ~たかった means 'wanted to.' Note that 着物 historically meant 'thing to wear' (literal: 着る + 物) and could refer to clothing in general; in modern usage it almost always points to the traditional Japanese garment.