Attainder

"I charge you to bring the King’s justice to the false knight Gregor Clegane, and all who shared in his crimes. I denounce him and attaint him, I strip him or all rank and title, of all lands and holdings, and sentence him to death."

- Hand of the King Eddard Stark

'Attainting is a royal decree made by the King of the Andals and the Fire Men, officially denouncing a person or an entire noble House.

To attaint a person or family apparently involves stripping them of all lands and titles.

In the books
In the A Song of Ice and Fire series, the manner in which Eddard Stark denounces Gregor Clegane is similar, but from what little context is given in the scene it wasn't clear if "attaint" was simply being used as a synonym for "denounce" or if it signified a specific, formal action.

The prequel novella The Princess and the Queen, covering the events of the civil war known as the Dance of the Dragons which occurred 170 before the War of the Five Kings, made it explicitly clear that "attainting" is indeed a specific legal action. At one point when the war had turned in favor of Rhaenyra Targaryen, she told her advisors that she wanted to attaint those Great Houses who had sided with her half-brother Aegon II Targaryen. Specifically, she wanted to attaint House Lannister and House Baratheon, and give their lands away to her own loyal supporters.

What exactly "attainting" includes isn't clear, as other Houses have had their lands seized before as punishment. Whatever the case, Rhaenyra's own advisors felt that attainting was such a shockingly brutal move that they pleaded with Rhaenyra not to do it, saying that it would set a bad precedent and discomfort her current allies.