Someone who isn't very attractive, but isn't horrible.
A male/female who isn't attractive earlier on in the evening. However, when 2 am comes along and the bar/club starts to close, you are willing to take him/her home.
2AM can be used anytime of the day.
Friend- "What do you think about him/her"?
You- " She/he is a 2 AM"
Meaning: No thanks! I'm not that desperate yet.