Back then, when we were only aware of the black and ties, the word formal was only associated with these forms of dressings. So basically, formal dressing is a word used for proper vintage western attire or clothing for very fine occasions. For example, formal dressing is commonly observed at high-end functions and occasions like Easter, Christmas, and weddings, etc. not only these functions but on other big occasions like horse racing, balls, and dinners people are used to be seen in the formal dress code i.e formal hairdo both for men and women, dress pant in a dress shirt and a coat with a nicely tucked in a tie. Most formal dressing includes:

Court dresses
Diplomatic uniforms
Academic dresses
Full dress uniforms
Religious clothes
National costumes

https://en.wikipedia.org/wiki/Formal_wear