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!
The strong sunshine damaged my skin.
Underwear is often made of delicate fabrics, so washing and drying them at high temperatures can damage the fabric.
Hair dye damages your hair.