Especially between two walls or buildings, or sometimes (in the countryside?) lined with trees. A sense of it being an enclosed passage, regardless, as opposed to something more open. A lemony snicket would, no doubt, be one lined with citrus trees, though of course a Lemony Snicket is another beast entirely -- and it would be best to avoid any unfortunate events by going down that road. Origin is, as all too common with this sort of old slang, entirely unknown, first recorded in the late 19th century.
Pub's down't road, first snicket on't right, pas't badger and on't left.