No, this isn’t a geographical term: it’s a specific method of distillation. The legal definition – enshrined in EU law – prohibits “post-distillation additions”. So, to be called a London dry, a gin must not have had anything added to it once it comes off the still (although exceptions are made for water and neutral spirit, to get it to bottling strength). That means no infusing, no added sweeteners, no colouring, and also no cask-ageing.
This ‘pure’ method of distillation generally leads to gins that express the clearest ‘ginny’ flavours. Because it is a production technique, not a geographical indication, London dry gins are produced all over the world, from San Francisco to Syndey to Singapore (sometimes distillers suffix ‘Dry Gin’ to their own geographical location, to indicate that this production method has been used).