The various Indian tribes of the Black Hills region had been given until January 31, 1876 to voluntarily report to their new assigned reservations. The U. S. military was assigned to round up all delinquent tribes, including the Sioux, Arapaho and Cheyenne. Hunkpapa Lakota chief Sitting Bull had called a meeting of these holdouts along the Little Bighorn River. It was part of Lt. Colonel George Armstrong Custer's detachment of the 7th Cavalry Regiment that stumbled upon this large group of hostiles. Custer had less than 600 troops separated into three large battalions and several other small detachments. Combined Indian forces range from 1000-5000; in any case, the usually thorough Custer was heavily outnumbered when he ordered the ill-timed assault.
Following the massacre at Custer's Last Stand, the Lakota and Cheyenne regrouped and attacked the remnants of Custer's command led by Major Marcus Reno and Captain Frederick Benteen. They held off the attacks (until reinforcements under General Alfred Terrry arrived), and both of these officers survived the fighting. The victory was a hollow one for the Native Americans, however. A renewed effort by the military forced Sitting Bull's followers into Canada, where they remained exiled for nearly four years. The remaining 200 Lakota headed south, where they surrendered in July 1881. They were housed at the Dakota Standing Rock Reservation after some shuttling for fear of another uprising.
Sitting Bull eventually appeared in Buffalo Bill's Wild West Show, while Custer's death cemented his place in American military lore.
Your question specifically refers to the effect of the battle, so I'll try to concentrate my perspective on that. It's great and interesting history about Custer himself, as he was such a personality, and the battle - fighting against overwhelming odds and finally, a story of the Native tribes winning! Can't beat that for interest level.
But the effect of the battle was to cause the US government and military to concentrate forces on the northern Sioux tribes and bands and to make a serious effort to "pacify" Montana. The wars against the Sioux and Crow tribes in the region were the last major Indian wars fought in the US, culminating in a massacre at Wounded Knee in 1890 that many suggest was revenge for Little Big Horn.
The major effect of the Battle of the Little Bighorn (where Custer and his men got annihilated) was that it really got Americans in general very angry at the Indians and much more motivated to end the wars. It really did the Indians no good at all except in a temporary sense.
As to causes, it happened because gold had been found in the Black Hills and settlers were moving in even though it was Indian land. The Indians were then forced to move to a smaller reservation, but some did not want to go. This led to the battle.