It means something different in each department but the basics are that you are essentially able to do the dept head's job and be his backup on a daily basis. Once you have done the job for a while and have met all the corporate requirements for qualification, you become a "qualified" backup.
It's a vague question for sure. In my zone we have Assistant's but not all are qualified. Some don't know how to cut meat, some are great meat cutters but struggle at using a computer. They have these "training programs" that teach "team building" and how not to sexually harass someone but won't teach you "your job".
Well, in the movie industry they're sometimes called fluffers. I don't know that there are any special qualifications, other than a moist mouth and a steady grip.