This name has become a part of pop-culture used to describe any personal assistant position (read: practically a slave) in allusion to the character "Emily" from the movie "The Devil Wears Prada".
She was Miranda Priestly's personal assistant and it was the name the main character (Anne Hathaway) was often called after by mistake (as she wasn't appreciated enough for her boss to bother to learn her real name).
This is someone who works very hard and is always doing a million things for their boss and their work is never appreciated.
A: Ugh, I had such a rough day today at work! I had to take care of a million things!!!
B: Wow, that sucks!
A: Yeah, I'm like my office's Emily!