When a female physicly lifts someone and then carries him/her around. It usually refers to a woman lifting a man, but it could be a woman lifting a woman, too. The phrase is most often used to describe a fetish for this.
John: Didn't you find it humiliating when that bodybuilder chick picked you up and carried you around the room?
Dean: No, I liked it; I have a lift and carry fetish.