Can't read the handwriting, sorry, though it looks like it might be from 1883 judging by the number at the foot of the letter. Hesse(n)-Nassau (on the placard held by the group in pic one) was a province of the Kingdom of Prussia from 1868 to 1918, then a province of the Free State of Prussia until 1944.

Edit: There also seems to be another sign, slightly washed out. The text reads something similar to 'Kreigerverband Grafsch Schaumburg' - Warrior detachment..? Seems likely they are military veterans. There is a place in Germany called Schaumburg.

Edit2: Added letter date/formatting.

Edit3: Some of them seem to be wearing medals which resemble these Prussian Warrior League Medals. The text on the black and white ribbon looks to read 'Preussicher Landes-Kriegerverband'. Nearest reference I can find translates as 'Prussian Country's Warrior League', but that name only came into use in April 1897, after the apparent date of the letter.

Edit4: u/Comrade-Chernov clarifies the name translation in this post. "Prussian regional veteran association".

Hope this can help start someone else off with more specific info on who is pictured and what they are doing.

Well, I can't read a word on the back of the card, so there's that. I'll go off of what I can make out in the picture.

The sign in the background seems to say "Kriegerverband Grafsch. Schaumburg", or "Veteran association, County (of) Schaumburg".

The sign in the front reads Hesse-Nassau - a province of Prussia which was created in 1868 and would indeed have included the area of Schaumburg. So here we have a photograph of a war veteran organization from Schaumburg, Hesse-Nassau, which means the war these men would have had to have taken place after 1868 in order for them to be under the Hesse-Nassau banner.

So, with that in mind, I'm assuming these men are veterans of the Franco-Prussian war. The Prussian army at the time recruited units based on geopolitical entity, so these men likely served together, or at least under the same overall commands. Most likely they belonged to either the Prussian 9th Corps (which contained an entire infantry division recruited from Hesse) or the 11th Corps (which contained, among others, 6 Hessian and 2 Nassauer infantry regiments).

The writer didn't care about punctuation or correct spelling, so it's not all that easy. Not sure what he means by "main", it could also refer to "head/face". The "flag" likely refers to "banner", i.e. the group of people.

This card was photographed by a colleague at the stadium. The banner [=group of people] coincidentally was where all other banners had stood in formation. Hopefully, you will find me and [Mr.] Haupt. All thos who ^have hats and wind jackets(?) are Kintler(?). The one with the full beard is the ~commissioner Roda, 83 years old.

If the other guy is right and it's from 1883, could be an event for the veterans of the German unification wars.

I can't read the script, but there are guys over at the genealogy subreddit who can, it's called Kurrent and was the standard German style of handwriting back then. If you post this over there someone will help you out eventually.