With regards to the word 方言 popularly taken to mean "a dialect", a definition of the word "dialect" is necessary.
A dialect is defined as "A particular form of a language which is peculiar to a specific region or social group" So, it is a "form of a language", meaning it has a "mother language" and it takes on a certain "form", branching off from the mother language owing to particular regional usage over time and reasons of geography.
From this dictionary definition of dialect, does 方言 mean or equate to being a "dialect"?
方言 is made up of 地方 & 语言, meaning the "language" of a particular place or locality. Not the "branching off from a certain mother language owing to particular regional usage over time and reasons of geography", like, say, the branching off from Mandarin, (the mother language), giving rise to a regional dialect called "Candarin", spoken by Chinese immigrants in a country called Canada.
Thus I would argue that the word 方言 as I understand it does not fit, for reasons of strict definition, into the notion of a "dialect"
However, the popular understanding is that 方言 means "dialect". And I have oftentimes translated it as such. I am sure I'll be punished by the God of Linguistics.