A military expression referring to an issue that the speaker wants to address, but recognizes would be too much hassle to deal with. It's a metaphor for realizing that, although you want to defend your "hill" from attack, to do so would be suicidal given the much stronger enemy, and this particular hill isn't so vital that you should give up your life for it, so it's best to just retreat.
- "The Colonel wants to kick off the exercise on Monday, but we're really not going to be ready until at least Tuesday. But that's not a hill I want to die on, so I'm just going to go along with what he wants."
- "Look, I understand you're upset about them demoting Corporal Thompson, and I know you want to go argue his case with the Sergeant Major, but is that really a hill you want to die on?"