The Weather Underground was an organization founded by Bill Ayers and Bernardine Dohrn. They intended to "Bring the War Home" by inflicting on American soul what they believed the military was doing on Vietnamese soil. They started a series of riots in Chicago called the Days of Rage.

Because of these tactics, they were hated even by other radical groups. Fred Hampton, head of the Black Panthers told his people that he wanted nothing to do with them. A few weeks later, Hampton was killed in an FBI raid, and the weathermen decided it was time to go to war against the US. They detonated a bomb in the Pentagon, though nobody was killed. They also planned on setting off a nail bomb at a military dance, but the three conspirators were killed when they accidentally detonated it at their own home.

With the end of the war, the organization slowly disbanded. The leaders were given very light sentences in a deal that was made with them: the government would let them off if they let the government off from illegal FBI spying. Ayers eventually came to regret what he did and started teaching at the University of Illinois, where he became acquainted with Obama, which caused quite a controversy. Many conservatives still believe that Obama's memoirs were ghost written by Ayers.

For some reason, there is a current organization also called the Weather Underground, which tells us the weather. The two are not related.

Edit: Most of the Weathermen's more violent activities came after, and in response to, Hampton's death at the hands of the FBI. The leaders of this group were never imprisoned.

Sources:

http://historynewsnetwork.org/article/93754

https://www.thenation.com/article/remembering-left-wing-terrorism-1970s/

https://www.fbi.gov/history/famous-cases/weather-underground-bombings