Dialect
noun, の adjective
The way you say things could be translated as your accent... but this is much bigger. This is an entire "way" of speaking. This is a dialect.
You can even think of the 方 as being "direction" where you go in different directions in a country and discover different dialects, if that way of thinking helps.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
このエリアの方言で「ありがとう」は何と言いますか?
How do you say "thanks" in the dialect of this area?
この国では方言がとても大切にされています。
In this country, dialects are cherished.
日本の方言を学ぶことは、日本文化を大切にすることです。
Learning Japanese dialects is valuing Japanese culture.