Fetching details from the dictionary...

to pierce; to penetrate; to soak in; to permeate
to sting (wound or sensitive area, etc.); to smart; to twinge
to be infected (with vice); to be steeped (with prejudice); to be influenced
to feel keenly; to make a deep impression
出汁の味が大根にしっかり浸みた。
The flavor of the broth has fully soaked into the radish.
長年の雨水が壁の奥まで浸みていた。
Years of rainwater had seeped deep into the wall.
醤油が服の繊維にまで浸みてしまった。
The soy sauce soaked all the way into the fabric of my clothes.