To Damage Something
To Injure Something
transitive verb, ichidan verb
The kanji means wound, and this verb is transitive, so it means to damage something or to injure something.
You can use it to talk about parts of your body, so you'll sometimes see it used interchangeably with 痛める. The difference is that it's objectively focussing on the damage, not the pain. That's why 傷める can be used for objects like cars and furniture, too, whereas 痛める is only for people and body parts.
You learned this reading when you learned 傷む. Yay!
強い日差しに当たってはだを傷めてしまった。
The strong sunshine damaged my skin.
下着はデリケートな生地を使っていることが多いので、高い温度での洗たくや乾そうは生地を傷める原因になる。
Underwear is often made of delicate fabrics, so washing and drying them at high temperatures can damage the fabric.
染毛剤は髪の毛を傷める。
Hair dye damages your hair.