The complete answer to this question could fill a whole book! Luckily, I am writing such a book right now. In the meantime, here is a shorter answer to get you started:
The Black Panther Party was a nationwide organization that existed in black communities in the United States from 1966 until about 1982. The Panthers played several roles in these communities: they were civil rights activists, community organizers, and could even be called a political party. The Panthers created community service programs like free breakfast programs and free health clinics for people in need, and they patrolled poor black neighborhoods to protect citizens from police brutality, which was common at the time. Most of the Panthers were young black Americans who had grown very frustrated with racism in their communities, so they decided to take action to change the way people thought about race in America. Unlike the civil rights movement activists before them (who all committed to non-violent passive resistance) the Panthers carried guns and believed equality should be defended by any means necessary, a philosophy which remains controversial to this day.