What is "see a man about a dog"

vb. (context idiomatic English) (non-gloss definition: Used as an excuse for leaving without giving the real reason (especially if the reason is to go to the toilet, or to have a drink).)

To see a man about a dog or horse is an English idiom, usually used as a way to say one needs to apologize for one's imminent departure or absence—generally to euphemistically conceal one's true purpose, such as going to use the toilet or going to buy a drink.

The original, non-facetious meaning was probably to place or settle a bet on a racing dog.