I care about baseball about as much as I care about industrial cheese-making technology, but.
A twinight (twilight + night) baseball game is a doubleheader that starts in late afternoon as opposed to one that starts in late morning so that the second game is played at night. The term can also refer to the first game of the same.
Because somebody's gonna ask, the second game of such a doubleheader is called a nightcap.