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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
柑橘類の果汁が手の傷口にしみて痛い。
Citrus juice stings when it gets into the cut on my hand.
祖母の優しさが胸にしみる夜だった。
It was a night when grandmother's kindness touched me deeply.
疲れた体に温泉がしみるように感じた。
The hot spring felt as if it soaked into my tired body.