Expedition to The Black Hills is a decision unique to 
USA. It paves the way for the event chain The Sioux Wars including Little Bighorn and End of the Sioux Wars. The event chain will eventually lead to Dakota being added as an accepted culture.
It shows up in the tab after 1874, if USA owns Rapid City, South Dakota (ID 122), which it does at the start of the game. Then all USA has to do is to place troops there. It gives 1 prestige, which is not a lot, but on the other hand it is not very hard to do. The event Little Bighorn removes 5 prestige so one should not take it to get prestige, but either for role playing reasons or to eventually add Dakota as an accepted culture.
The event The Sioux Wars can happen after the RGO has changed to 
precious metal. It has a mean time to happen of 1 year and gives all Dakota POPs a militancy of 8.
America should be able to deal with any rebels as there is not a lot of Dakota POPs even though 8 militancy is quite a lot. The Sioux Wars will end by the event End of the Sioux Wars, which requires, that there are no rebels in the entire country, and it has a mean time to happen of 2 years.
In the game files it is called Custers_expedition instead of Expedition to the Black Hills