There was once a powerful noble house called House Reyne with a Red Lion as a sigil (as opposed to the Lannister's Gold Lion). They were the Lords of Castamere. They were also the second wealthiest House in the Seven Kingdoms, behind only the Lannisters. They had a rebellion against their Liege Lord, Tytos Lannister. House Reyne was eradicated. Not a single member of the family survived.
The Rains of Castamere was a song written about the event. "Rains" and "Reynes" are switched in a bit of wordplay.
From the ASoIaF wiki:
During the reign of Tytos Lannister the Lord of House Reyne rebelled against his overlord along with the Tarbecks of Tarbeck Hall. The Lord of House Reyne was an experienced warrior while Lord Tytos was rather weak so it appeared that their rebellion could be successful. In the end Tytos's young son and heir Tywin Lannister held the command of the Lannister army. Tywin besieged the castles and destroyed the rebels. After the rebellion the seats of the rebels were brought down and both houses were completely exterminated.
It is not known if the rebels died in acts of war or that they were executed.
And the lyrics:
And who are you, the proud lord said,
that I must bow so low?
Only a cat of a different coat,
that's all the truth I know.
In a coat of gold or a coat of red,
a lion still has claws,
And mine are long and sharp, my lord,
as long and sharp as yours.
And so he spoke, and so he spoke,
that lord of Castamere,
But now the rains weep o'er his hall,
with no one there to hear.
Yes now the rains weep o'er his hall,
and not a soul to hear.
The "proud lord" in the song is Lord Reyne.