If someone is oversensitive, they are easily upset or offended. A small joke, a short email, a look — and they feel hurt, or they think you meant something unkind. Sensitive already means feelings bruise easily; the over- makes it “too much of that,” at least in the speaker's view. People often say it as a complaint: “Don't be so oversensitive.” That can be unkind. Though actually, what looks like too much feeling from outside can be a real hurt on the inside, or a person who has been hurt before. Younger speakers may just say too sensitive. The over- makes the judgment louder. This sense is about feelings, not about a clever mind.