expression, noun
that road; that path; that way
Refers literally to a specific road, path, or route already mentioned or understood from context.
その道をまっすぐ行くと駅に出ます。
If you go straight along that road, you'll come to the station.
expression, noun
that line of work; that profession; that trade
Used to refer to a particular field, occupation, or area of expertise, often in contexts like その道の専門家 (an expert in that field).
See also: 道
彼はその道のプロだ。
He's a pro in that line of work.
その道にくわしい人に相談したほうがいい。
You should consult someone knowledgeable in that field.
expression, noun
love affairs; romance
Euphemistic or indirect way of referring to romantic or sexual matters, similar to 'that department' in English. Often used in phrases like その道の話 (talk of romance).
彼はその道の話になると急に黙り込む。
He suddenly goes quiet when the topic turns to romance.
道 is the general word for 'road' or 'way'; その道 specifies 'that road' or, idiomatically, 'that field/line'.
Phrase composed of その (that) + 道 (road, way). The figurative senses (profession, romance) developed from the idea of 'that path/way' as a specialized domain or course of action.