The rifle was developed by two Norwegians, Colonel Ole Herman Johannes Krag and Erik Jørgensen. They tried to interest their own country, but the first nation to adopt the rifle was Denmark, in 1889.
In the 1890 period, the U.S. was looking for a repeating rifle to replace the single shot, .45 caliber rifles (called "trapdoors" for the way they opened for loading) that had been in use since 1873. An Army commission tested various rifles, and selected a modified Krag-Jorgensen as the one they felt would best meet American needs. They also chose a new, .30 caliber cartridge loaded with 40 grains of the then-new smokeless powder; the cartridge was called the .30-40 on the commercial market.
The rifle was officially adopted in 1892, but production at Springfield Armory, in Massachusetts, did not begin until 1894. The rifle served in the Spanish-American War, but was in short supply and some volunteer and militia units were armed with the old rifles. All U.S. Krags were made at Springfield; none were made anywhere else.
There were three basic rifle versions, the Model 1892, Model 1896 and Model 1898, although the differences were minor. There were also carbines of each model as well as Model 1899 carbines. The carbines had shorter (22" vs. 30") barrels than the rifles to make them more usable for the cavalry.
Since the "Krag", as it was usually called, was in use in the period when America became a world power, it has often been associated with, and been made a symbol of, that expansion. One example is a poem about American action in the Philippines, with the refrain "Underneath the starry flag, civilize 'em with a Krag." Since the main opposition in the Philippines came from the Moros, who were Moslem, and who fought with the same fury as modern Jihadists, there is a bit of "deja vu" in discussing that period.
Krags remained in service until after WWI, although none were used in combat in that war. The Krag was replaced by the Model 1903 Springfield, also a .30 caliber bolt action rifle, but one that was much more powerful.
Incidentally, Norway did adopt the Krag-Jørgensen as its service rifle in 1894 and kept it until after WWII.
Like most former military rifles, Krags have become valuable collectors' items, being associated with a time when America was forced into a new role in the world.
HTH
Jim