What's the meaning of the phrase 'Fag end'?
The remnant of something, especially the part left after the best part has been used.
What's the origin of the phrase 'Fag end'?
For most of the 20th century in the UK cigarettes were known colloquially as fags and a fag-end was the name of the end part of the cigarette, after most of it had been smoked. It feels intuitively that the cigarette is the source of the more general term 'fag end' meaning 'the left-over part of something'.
That's what I was expecting to find when I started to research the expression. However, it turns out that, as well a 'cigarette', the word fag has several other meanings, which are:
The end of a roll or bale of cloth.
A parasitic insect that infects sheep.
The junior member of a group who performs menial tasks.
A homosexual man (a shortened form of 'faggot').
So, it could be that 'fag end' derives from one of those meanings. A little more delving showed that the 'fag end' was the name given to the last piece of cloth on a roll well before cigarettes were thought of. For example, the term is found in this piece from the English preacher George Bury's book of sermons The Narrow Way, 1607:
Mercers and Drapers neuer shew vnto their chapmen the middle part & fag end of their wares, but onely the vpper part thereof which commonly is very good.
[Note: a mercer was a trader in cloth and fabric.]
So, rather than fags (cigarettes) giving their name to 'fag ends' it was the other way about. Fag ends (of cloth) gave their name to any small remnant and so the end part of a cigarette took on the name fag end, which subsequently caused cigarettes to be called fags.
This process took some time. Fag ends were named in the early 17th century but it wasn't until the end of the 19th century that fag ends and then fags were used to refer to cigars and cigarettes.