From The Fellowship of the Ring, book II, chapter II, page 273:
'And not so many, nor so fair, as when Thangorodrim was broken, and the Elves deemed that evil was ended for ever, and it was not so.'
What does "broken" mean here?
This refers to the War of Wrath during the First Age. Thangorodrim referrred to three volcanic peaks raised by Morgoth (see chapter 9, "Of the flight of the Noldor" in The Silmarillon) Chapter 24, "Of the voyage of Eärendil and the War of Wrath", explains (emphasis added),
But Eärendil came, shining with white flame, and about Vingilot were gathered all the great birds of heaven and Thorondor was their captain, and there was battle in the air all the day and through a dark night of doubt. Before the rising of the sun Eärendil slew Ancalagon the Black, the mightiest of the dragon- host, and cast him from the sky; and he fell upon the towers of Thangorodrim, and they were broken in his ruin.
In other words, when the great dragon Ancalagon was killed, its fall crushed the towers of Thangorodrim.