Orthanc is the black tower of Isengard.
Orthanc was built during the Third Age by the Númenóreans of Gondor out of a single piece of stone by an unknown process and then hardened. No known weapon could harm it. Orthanc rose up 500 feet above the plain of Isengard, and ended in four sharp peaks. Its only entrance was at the top of a high stair, and above that was a small window.
Orthanc housed one of the palantíri of the South Kingdom, and was guarded by a special warden until Isengard was mostly abandoned by Gondor around the time of foundation of Rohan. After that the tower was locked.
When Beren, Ruling Steward of Gondor gave Isengard to Saruman, he also gave the keys to Orthanc to the Wizard. Saruman made it his base of operations during his search for the One Ring and later his attack on Rohan during the War of the Ring. After Saruman's defeat he was confronted by Théoden King, Gandalf and Aragorn, at which time Gríma Wormtongue, Saruman's servant, threw the Palantír at the group trying to kill them. Saruman was then locked in Orthanc and guarded by Treebeard, but subsequently escaped.
During the Fourth Age Orthanc was searched by Aragorn King Elessar, and he found there many heirlooms of Isildur, among them the original Elendilmir, the Star of Arnor, which proved that Saruman had found (and probably destroyed) Isildur's remains. Aragorn also found there a casket which obviously had been intended to hold the Ring.
- "A great ring-wall of stone, like towering cliffs, stood out from the shelter of the mountain-side, from which it ran and then returned again... one who passed in and came at length out of the echoing tunnel, beheld a plain, a great circle, somewhat hollowed like a vast shallow bowl: a mile it measured from rim to rim. Once it had been green and filled with avenues, and groves of fruitful trees, watered by streams that flowed from the mountains to a lake. But no green thing grew there in the latter days of Saruman. The roads were paved with stone-flags dark and hard; and beside their borders instead of trees there marched long lines of pillars, some of marble, some of copper and of iron, joined by heavy chains.
"...to the centre all the roads ran between their chains. There stood a tower of marvelous shape. It was fashioned by the builders of old, who smoothed the Ring of Isengard, and yet it seemed a thing not made by the craft of Men, but riven from the bones of the earth in the ancient torment of the hills. A peak and isle of rock it was, black and gleaming hard: four mighty piers of many-sided stone were welded into one, but near the summit they opened into gaping horns, their pinnacles sharp as the points of spears, keen-edged as knives. Between them was a narrow space, and there upon a floor of polished stone, written with strange signs, a man might stand five hundred feet above the plain."
- ― The Two Towers, "The Road to Isengard"
In Sindarin, it means for "Mount Fang", containing root or and the word anc "jaw". In Old English (used to render Rohirric) orþanc or orþonc means "intelligence, understanding, mind; cleverness, skill; skillful work, mechanical art".
However another curiosity arises in that although Old English is used to "translate" Rohirric, the Rohirrim did not speak Old English per se. We can suppose that while "orthanc" was an actual word in Sindarin, it also had a different meaning in original Rohirric (although its etymology is not given) and "coincidentally" also in Old English.