Vitae is Latin for "Life" so for academics their academic vitae is their professional life on paper. It is similar to a resume but different in some important ways. It does list degrees earned and often may include other institutions that the faculty member has worked for. But the main focus is on what the person has taught and the ideas that person has presented and published. The implication is that one will lead a life of contribution to the discovery and dissemination of knowledge.
Here's a link to my vitae. If you'd like to chat about any of the ideas I've presented or published, drop by anytime!