1. withdraw from a particular idea or course of action
back down from a fight/argument
When you 'back down' from something, you decide not to continue to challenge the position or opinions of someone else or uphold or fight for your own position or opinion. This usually occurs as a result of pressure from others. You might 'back down from a fight' or argument, for example. A more advanced word meaning 'to back down' is 'concede'; as in "The government conceded to the protesters and changed the unpopular law". You can use 'back down' in social or professional contexts, in numerous situations; but 'concede' is more formal.