Literally means for one head. In the context of tango lyrics it means by a head of a horse. The music is originally composed by Carlos Gardel and the lyrics are written by Alfredo Le Pera.
Por una Cabeza tells the story of a gambler who compares his lack of luck with women to a horse race where the difference between winning all and losing all is a matter of one head of a horse.
This music is in Scent of a Woman, Schindlers List, and True lies
The tango theme is said to be similar to a theme from Mozart's Violin Rondo