When Mononobe Yuu fights Hecatoncher, Yggdrasil tells him he needs to give up more memories because he has an "Incomplete Marduk".
In mithology, Marduk is the Babylonian god that fought Tiamat.
Also wikipedia erroneously names Yuu's cannon as Marduk. The cannon's name is Babel.
In Juuou Mujin no Fafnir, Yuu contracts with the oldest Dragon Yggdrasil. This allows him to get blueprints for weapons from an ancient lost civilization. If you look carefully, all of the weapons are names of Mesopotamian myth, especially with Babylon. If you know Babel, it was attributed to the Mesopotamian god Marduk (not Babel, but associated with a similar structure Etemenanki).
So essentially, Marduk is a huge weapon and Babel is its main cannon which stops Leviathan. As nhahtdh pointed out in the comment, Megiddo and Noah are the other cannons. So to complete the whole weapon Marduk, he needs to give up more memories. In essence, you can think of Marduk as a huge battleship and Babel as one of its cannons.
For Tower of Babel allusions: Tower of Babel - Wikipedia
According to Juuou Mujin no Fafnir article on Japanese Wikipedia (I find the Japanese articles on recent anime rather detailed, compared to the equivalent article in English):
Marduk
As the trump card in the fight against Dragon, it's an anti-Dragon weapon used by Mononobe Yuu from time to time. Among the weapon blueprints obtained from Yggdrasil, its main armament is impossible to be reproduced by the current scientific technology [..] Being technology of previous civilization once existed in the far past, none of those blueprints still remains in the modern time.
Although the original Marduk is huge weapon consists of many types of batteries1, it's not possible to completely materialize the whole weapon with the power of D. However, it can be used in battle by materializing the only the minimal necessary part of the battery.
To date, the batteries featured so far are the special cannon Megiddo (Boundary-Scorching Blue Flame) which annihilated Hecatoncheir, the main cannon Babel (Sky-Blocking Tower) which annihilated Leviathan, the twin gun Noah (Equinox-Lasting Ark) which annihilated Hresvelgr. [...] It's currently not known whether these three cannon makes up the whole of Marduk or not.
1 Meaning a fortified emplacement for heavy guns. Translated from 砲台.
Translated from article version dated 2015-05-03. Some text removed due to conflict with knowledge from other source, or not related to the question being asked.
As stated in the Wikipedia article, Marduk is the name of the whole weapon, which Yuu only materialize parts of during the fights against Dragons. Megiddo, Babel and Noah are the names of the cannons on Marduk.
