I was reading a book and there was a throwaway line about Count von Zeppelin being an official war observer for Germany in the American Civil War. I looked up this position and was surprised that it was fairly common. I was curious about how it arose, how it worked, and why it even happened in the first place. Being a war observer seems like a crazy idea and I was surprised that countries allowed other nations to watch their conflicts and armies.
Letting other countries observe your army served both as a negotiating tool and a bit of prestige.
There was a lot of money to be made in showing off what your country could do as a manufacturing power house. As it were, in the 1800's building a good quality rifle at a reasonable cost that wasn't maintenance hungry was an art more than a science, and buying the period equivalent of a "paint by numbers" book to building such a gun was quite the investment.
And it was also a way of showing off. Kind of like how nuclear tests today are used by North Korea to demonstrate that they are very serious and need to be taken seriously or else they will seriously use their serious nuclear weapons, seriously, 200, 300 years ago an army might allow observers to throw their weight around. "This is what our army can do. We have 10 soldiers for every 4 of yours. You may want to negotiate with us."
Similarly, it also let friendly countries keep up to date in terms of training methods, and war tactics. I mean, a big part of what made Napoleon so capable was his ability to control his army, and how he handled it's organization.
Quite the opposite, keeping your country's fighting capabilities a secret is often a bad idea. Something like WW2 or the US Civil War became as drawn out and bloody as they were because no one had a good idea of just how capable the other guy was of fighting. The north (and the south) thought the war'd be over in a few months, at worst, when things started out. Hitler and his fan club assumed the Soviets would negotiate kind of like how France threw in the flag from the huge display of force. But just like how the South likely had no concept of Lincoln's determination (or Sherman's tendency to wreck anything and everything) Hitler likely wasn't counting on the US crapping out so many heavy bombers that many German cities were more than half destroyed by them. Or that the Soviets would have so many reserve units they could call on.
Today armed forces have joint fighting exercises all the time and it's often a lot more to do with showing what your army is capable of than as legitimate training exercise.