Able to take criticism, insults, or unkindness without being hurt by them — as if your skin were too thick for the words to get through. It is normally a compliment, or at least neutral: it praises toughness. You hear it most about jobs where people get attacked a lot: You have to be thick-skinned to be a politician. A journalist needs to be pretty thick-skinned. It is also used as advice to someone who is taking things too hard: Try to be a bit more thick-skinned about the comments online. But watch the edge on it — because the picture is of a person who does not feel things, it can occasionally tip into a criticism meaning insensitive, someone who does not notice they are hurting others. Context tells you which. Its opposite, thin-skinned, is always negative: it means easily offended, quick to take things personally. Register is ordinary everyday English; it is fine in writing and at work, and it is a set idiom, so it is always hyphenated and always about emotions — never about actual skin.