1To penetrate or soak into something; to permeate or be absorbed (liquid or color).
雨で靴が濡れて中までしみてしまった。
My shoes got wet in the rain and soaked all the way through.
この布は水をよくしみるからコースターに向いていない。
This cloth absorbs water well, so it's not suitable as a coaster.
赤いインクが紙にしみて文字が読めなくなった。
The red ink bled into the paper and the text became unreadable.
2To sting or smart (as with a wound, sensitive area, or eyes); a sharp, burning pain.
目に香水が入ってしみるので洗ってください。
Perfume got in my eye and it's stinging—please wash it out.
傷口に塩がついてしみる。
Salt got into the wound and it stings.
3To be influenced or become tainted (metaphorically), e.g., to be infected by vice or prejudices.
悪い環境にしみてしまって考え方が変わった。
He was influenced by the bad environment and his way of thinking changed.
古い習慣が地域にしみついている。
Old customs have become ingrained in the region.
4To affect deeply; to leave a strong impression or feeling that touches the heart.
祖母の言葉が今でも胸にしみる。
My grandmother's words still resonate deeply with me.
映画の最後の場面が観客の心にしみた。
The final scene of the film touched the audience deeply.