The song title refers to "Buffalo", a group of photographers, models, musicians, hair and makeup artists, etc. formed by fashion stylist Ray Petri, of which group Cherry, Morgan, and McVey were all members. The song's title is also a reference to the Malcolm McLaren song "Buffalo Gals" (1983), which "Buffalo Stance" samples. Other samples came from Rock Steady Crew's "Hey You", and the saxophone break is from the band Miami's song "Chicken Yellow" (1974).
Cherry notably performed the song live on Top of the Pops while seven months pregnant. When asked by a reporter if it were safe for her to go up on stage performing, Cherry answered: "Yes, of course! It's not an illness." https://bit.ly/2t0hS3G