Thangorodrim was said to have been the piles of slag from Morgoth's furnaces and rubble from the delving of Angband, but at the same time they were solid enough to form sheer precipices; Maedhros was nailed to a cliff of Thangorodrim, and Hurin imprisoned on a high terrace. The tops of Thangorodrim perpetually smoked, and sometimes spewed forth lava.
At the base of the south face of the middle peak was the Great Gate of Angband, a deep canyon leading into the mountain, lined with towers and forts. There were also a number of secret gates scattered around the sides of the mountain group, from which Morgoth's hosts could issue forth and surprise their foes.
The position and size of Thangorodrim are unclear. One drawing by Tolkien, if to scale, would have made Thangorodrim 35,000 ft high, and the statement that it lay 150 leagues (450 miles) north of Menegroth puts it too far away for some of the action in The Silmarillion to make sense; a distance of 150-200 miles would have been more consistent.
Along with Beleriand and the entire west of Middle-earth, Thangorodrim was destroyed in the War of the Valar at the end of the First Age.