It basically means that we shouldn't question or analyse a situation but accept the decision. It's usually said when someone above us (eg. management, owner, etc) has made a decision which seems dubious or just strange. Instead of trying to find a reason, we simply say "our is not to reason why" and leave it at that.
Ours = our part in this. So "ours is not to reason why" can be expanded to: "our part in this situation is not to search for a reason as to why it is so".