Back Down Meaning

(idiomatic) To take a less aggressive position in a conflict than one previously has or has planned to.

Example:   I was about to sue them, but I had to back down.
  I was going to sue them, but now I'm going to have to back down.
2013 June 18, Simon Romero, "Protests Widen as Brazilians Chide Leaders," New York Times (retrieved 21 June 2013):
  By the time politicians in several cities backed down on Tuesday and announced that they would cut or consider reducing fares, the demonstrations had already morphed into a more sweeping social protest, with marchers waving banners carrying slogans like “The people have awakened.”