The name is a Spanish horse-racing phrase meaning "by a head", which refers to a horse winning (or losing) a race narrowly by just the length of its head. The lyrics speak of a compulsive horse-track gambler who compares his addiction for horses with his attraction to women.
Alfredo Le Pera was born in Brazil, son of Italian immigrants. Le Pera and Gardel died in an aeroplane crash in Medellín, on Monday, June 24, 1935.
"Por Una Cabeza" is featured in a famous tango scene in Martin Brest's film Scent of a Woman (1992), in the opening scene of Steven Spielberg's Schindler's List (1993), and in James Cameron's True Lies (1994).