(adj.) a term used to describe an immensely ugly person, usually referring to members of the other sex.
The ugly tree being the source of ugly people (to grow on the ugly tree like a fruit etc. is to be of undesirable appearance).
Bob: (points to a female) good lord my dear man, take a gander at yonder female, she is quite hideous I do protest!
Bruce: (in disgust) I must agree old chap, poor lady seems to have fallen out of the ugly tree!
Bob: I would go as far as to say she fell out of the ugly tree and hit every branch on the way down!
In general: to leave behind one's inhibitions or to behave in a way that is free from social limitations or any code of conduct.
(to let one's hair down)
Corrine Bailey Rae, Song:
Put your records on
Girl, put your records on, tell me your favourite song
You go ahead, let your hair down
Sapphire and faded jeans, I hope you get your dreams,
Just go ahead, let your hair down.