An elevator speech is a quick, 1-2 minute, presentation of yourself. In the time it takes to ride an elevator with someone, you should be able to present yourself in such a way that you have grabbed their attention in an interesting way and should succinctly tell the other person some highlights about your skills and interests.
The idea behind creating an elevator speech is to have a back-pocket summary of yourself so that no matter where you are, a party, at the worksite, or in an elevator, you are able to "sell yourself" and your abilities to a person that quite possibly can help you in your career!
Give it some thought. Just a few main points and how you'd get them across!