That's a rifle that's known as a Trapdoor Springfield. I am not a collector of them, or a real expert.
They were made for the US military post Civil War. The first ones used a relined CW Springfield musket barrel, with the rear cut away and the trap door mechanism installed. Those were 50-70 caliber, and date from about 1866.
The most common Trap Door Springfield is in 45-70 caliber. The 45-70 model dates from about 1873, I believe.
The Trap Door Springfield was replaced by the 1898 Krag, but some were still in use during the Spanish American war.
All of them are single shot, breech loading cartridge rifles using black powder cartridges.
The one you show seems to have been pretty well used- I would let a gunsmith check it out before you tried to shoot it.