RORY: Do you want to wear Docs or sneakers?
Rory is referring to Dr. Martens (or Doc Martens), a British brand of comfortable leather boots which have been a fashion accessory in youth culture since the 1960s. During the 1990s they were especially associated with the grunge movement.
The boots were first invented by Germany army doctor Klaus Märtens in 1945, and he began selling them in 1947. They were first brought out in the UK in 1960 after R. Griggs bought the patent for them. Dr. Martens ceased production in the UK in 2003 and moved their manufacturing base to Asia. Since 2004 a small amount of “vintage style” boots made to the original specifications are still manufactured in Britain.
Rory is often shown wearing Doc Martens boots during winter in the early seasons of Gilmore Girls.