Who was Chief Joseph of the Nez Perce tribe?

Chief Joseph was, as you say, a member of the Nez Perce tribe who lived in an area that is now made up of parts of the states of Oregon, Washington, and Idaho.  He is best known for having led a faction of the Nez Perce who resisted being pushed onto a reservation.  This faction attempted to make it to Canada, where they thought they could live as they wanted.  However, they were caught by the US Army in Idaho before they could reach Canada.  This was when Chief Joseph allegedly gave a speech that has helped to make him famous, one in which he supposedly said that his heart was “sick and sad” and that he would “fight no more forever.” 
Chief Joseph was born in what is now Northeastern Oregon in 1840.  His real name translates to something like “Thunder Rolling Down the Mountain.”  He was widely known as Young Joseph because his father was called Old Joseph.  His father had this name because he had been baptized at a mission in what is now Northern Idaho a few years before Chief Joseph was born. 
Old Joseph was one of the leaders of the Nez Perce.  As such, he had been very involved in dealing with the white authorities in what was then the Washington Territory.  In 1855, Old Joseph was involved in setting up a reservation for the Nez Perce in what is now Oregon, Washington, and Idaho.  This reservation was quite large and included much of the Nez Perce’s historical lands, including the Wallowa Valley, where Young Joseph was born. 
As was very common in the spread of the US across the continent, American authorities soon wanted to reduce the size of the reservation.  Gold had been found in the area and whites wanted the land for themselves.  In 1863, the American authorities proposed a new, much smaller reservation that did not include the Wallowa Valley and much of the Nez Perce heartland.  In another common historical occurrence, some of the Nez Perce accepted this new reservation and signed a treaty while others did not.  This led to a split in the tribe.
In 1871, Old Joseph died and Chief Joseph took over as leader of his band of non-treaty Nez Perce.  He continued to negotiate with US authorities.  In 1873, he got the government to agree that the Nez Perce could remain in the Wallowa Valley.  Four years later, however, the government changed its mind and the Nez Perce were ordered to leave.  Joseph’s band of Nez Perce was once again divided on the question of whether to go or to fight.  Joseph was inclined to avoid fighting, but others in the band killed a number of white settlers and the whole band decided to flee.
This is when Chief Joseph started to rise to fame.  For more than three months, the band of Nez Perce travelled through parts of Oregon, Washington, Idaho, Wyoming, and Montana, trying to make it to Canada, where Sitting Bull was living with a band of his people.  The US Army pursued the Indians as they went, and many battles were fought.  Chief Joseph is said to have led his people with great skill during this trek, which is often called the Nez Perce War.
Finally, in October of 1877, the Army caught the Nez Perce, who were largely out of supplies and exhausted, about 40 miles short of the Canadian border.  Chief Joseph surrendered, allegedly saying,

Hear me, my chiefs! I am tired; my heart is sick and sad. From where the sun now stands, I will fight no more forever.

However, as with many alleged speeches by Indian leaders, it is not at all clear that Chief Joseph actually spoke these words.  Whatever the truth is, Joseph became famous as the skillful war leader of the Nez Perce and as the eloquent speaker who finally surrendered his people for their own good.
Joseph continued to lead his band after they were captured and sent to Kansas and then to Oklahoma.  He tried to get the government to allow them to return to the Wallowa Valley, but failed.  Eventually, his band was sent to Northeastern Washington, where they lived on a reservation with Indians from other tribes in the region.  Joseph died on this reservation in 1904.
Chief Joseph, then, was a famous Native American leader of the Nez Perce tribe.  He is famous for having led his people on their trek towards Canada and for having fought brilliantly as he did so.  He is famous for the words that he allegedly spoke when surrendering, and he is famous for having constantly worked on behalf of his people until his death.
http://www.indians.org/welker/joseph.htm

http://www.pbs.org/weta/thewest/people/a_c/chiefjoseph.htm

https://www.biography.com/political-figure/chief-joseph