This is a very theoretical question, although I am sure the problem pops up in lots of IT and automation applications. Still, I prefer to formulate it in an action-movie scenario (a bit of the Prisoner's Dilemma style).
"You" and "I" are two groups of partisans hiding in two different places in the forest. The enemy are holding some of our guys in a heavily guarded prison. We want to attack the prison and free our comrades, but this can only succeed if both our groups participate. If just one group goes ahead, it will get massacred for nothing.
So we need to be sure we're both going for it. But the only means of communication we have are signal flares, and firing one does not guarantee it will be seen (due to distance, fog, whatever).
I leave aside the issue of the enemy seeing our flares, or firing their own to confuse us - it's just my flares and yours, and my eyes and yours.
Suppose I fire a flare meaning "I'm ready, are you?". You see my flare and you reply with another, meaning "Yes I'm ready too, let's go for it!". But I will only start if I see your flare, so you cannot start unless you are sure I have seen it. So now I need to fire another flare to confirm I have seen your reply...... and apparently this chain will never end. No matter how long we keep firing our flares, the last (and decisive) one will be unconfirmed.
Any ideas? For starters, does this problem already have a name that's recognizable in information theory?