Refers to the emotional strength needed to not be easily upset by criticism. As a stand-up comedian, she developed a thick skin against hecklers.
Pro Tip 2/3
Figurative Use
It's used figuratively to talk about emotional, not physical, toughness. Working in customer service requires you to grow a thick skin.
Pro Tip 3/3
Not Insensitive
Having a thick skin doesn't mean the person is insensitive, rather they cope well with difficulties. Despite being criticized, he showed he had a thick skin by responding kindly.