What is the purpose of the extension of the transverse white line (equivalent to the headstring in pool) beyond the 'D' to the cushions (rails)?
It seems to have no relevance to the game as played. The confines of the 'D' restrict the break-off shot and re-positioning of the cueball after an in-off (scratch) but the extension to the cushions of the white line seem to have no purpose.
It's called the "Baulk line" and shows the extent of the "Baulk" area. On a full-sized table the baulk-line is drawn 29 inches from, and parallel to, the face of the bottom cushion and denotes the area between the baulk-line and the bottom cushion including the "D".
The baulk area has no significance in Snooker and is only used in the game of English Billiards; an object-ball within this area is considered to be "In-Baulk", and cannot be played at directly if the striker is "In-Hand".
I often wonder why people use the Internet, to ask other users questions, the answers to which can be found.......on the Internet?
It has a benign function, which is dissemination of knowledge. I never knew that about the baulk line, nor did I know that I didn't know (to paraphrase Al Gore). But now I know. Might, of course be useless information.
If find those who knock Wiki to be in that boat. It has it's failures, but it's always a good starting point.
Wiki is as you say a good starting point but only for non controversial subjects, for example, one of the CAGW zealots who had editing rights decided that as the hockey stick obliterated the Medieval warm period and the little ice-age he'd better do the same in Wiki, it back fired on him eventually, and the original pages re-instated and he lost his editing rights, they also found he'd edited out references in the climate pages to papers that called CO2 into doubt for being the cause of the warming .