Green’s Dictionary of Slang

(orig. show business) a laugh, a joke.

1945		in Wentworth & Flexner DAS (1960) 49/2: [Scriptwriters are] always trying for a boff . . . a laugh.
1959		G. Marx letter 7 Dec. in Groucho Letters (1967) 211: I love playing it and hearing the boffs.
1962		S. Longstreet Flesh Peddlers (1964) 40: The new domestic family comedy [...] played for boffs and heart.
1978		Miami News (FL) 19 Oct. 13/3: ‘You get more boffs [...] who needs these rubes?’.
2000		Guardian Mag. 13 May 33: Hope marked them with a special code: [...] tick (‘boff,’ as he called a big laugh), tick with a line through it (super-boff), tick with two lines through it (super-super boff). He was always pushing for the big laughs.