What are a 'coach lines' So contacted a bike restoration place for a quote to respray my BSA, the guy asked me do I want 'coach lines'. Too embarrassed to ask what they were I just said yes.

So what are they exactly?
Coach lines (stripes) are a type of thin stripes you saw on (typically British) cars. They were a hallmark on high end cars like Rolls Royces.  

See this image from from this article:



The coach lines are the lines under the guy's hand.

See also the wikipedia article on Pinstripes. 

My guess is that this bike may have had some sort of pin striping.