。
She left the dirty dishes soaking in the sink.
Literal
She [topic-は] became-dirty plates [object-を] sink [in-に] soaked.
浸ける ('to soak/submerge') belongs to the same family as 漬ける, used for pickling vegetables — both mean putting something into liquid for an extended time. The location particle に here marks the destination of the soaking, not where the action takes place generally; with verbs of placement (置く, 入れる, 浸ける), に specifies the endpoint where something ends up. 汚れた is a past-form verb acting as an attributive: 'plates that have gotten dirty' = 'dirty plates.' 流し ('sink') comes from the verb 流す ('to let flow') — a fitting name for where water runs out.