Emperor Battle Titan
The Emperor Battle Titan is the second largest land based weapon the Imperium of Man, or any faction even, can field (the first is the Capitol Imperialis super heavy tracked vehicle). Comparable to an Imperial Cathedral on legs, depending on what sources you take from it stands between approximately 43-100 metres (130-330 feet) tall (including the cathedral spires), and is quite simply the most devastating vehicle ever seen on the many battlefields of the galaxy. It is seen as a physical manifestation of the Emperor's will, and just like the Imperium itself, once they are fully deployed, they are relentless, unyielding, and unstoppable. It is similar in size to a Starhawk bomber (the bomber is probably not as wide, though), which is a long-range void bomber utilised in squadrons for ship-to-ship combat, typical capital ships that carry these vessels can deploy upwards of 2 dozen of these in addition to support weapons, which should tell you just how ridiculously huge both space combat and the land based Imperator are.
Overview
Captained by only the most battle-hardened and elite of Princeps, its interior is large enough for it to serve as a mobile headquarters, with room for dozens of operators and serfs; it can also transport around a hundred Imperial Guardsmen or dozens of Space Marines in its lower legs for either close defense or to assault a shattered fortress.
The Emperor Battle Titan comes in two models: the standard 'Imperator' is an all-round assault and support vehicle, whereas the 'Warmonger' specializes in long-range fire support. The Imperator is commonly seen leading Titan assaults, while the Warmonger rains artillery on the foe with its city leveling firepower.
Their only difference is in weaponry; the Imperator have shorter ranged weapons, while the Warmonger is armed with long-range artillery and missile platforms. A third Emperor with an aircraft carrier deck on its back was planned and showcased as part of the buildup to the release of Titan Legions, but sadly Titan Legions was an overcomplicated trainwreck of a system and the planned line of super-Titan variants was canned as soon as people stupid enough to buy a box containing more counters than Battle for Armageddon realized this.
Chaos Emperor Titan
Most of the Traitor Emperor Titans have mercifully been destroyed, but the small handful that remain are as deadly as their Imperial counterparts, if not more so. Most of them have been possessed by Greater Daemons, making them essentially supersized Daemon rape Engines.
Origins
The Imperator was one of the two showcase Titans for the Epic expansion Titan Legions, which aimed to take the system back to its Adeptus Titanicus roots of having small numbers of really expensive models battle it out rather than large numbers of dirt-cheap plastic infantry and tanks. Coming in the heyday of the Second Edition "moar rules = bettar" design philosophy, the Imperator came in a box with roughly half a dead forest's worth of cards, counters and rules and featured an insidiously complicated double-sided datacard for the player to perpetrate accountancy on every turn with plasma tokens and garrison troops and a whole load of other shit that made firing a Conversion Beamer in Second Edition seem simple by comparison.
As usual for Titans, the Imperator was roughly 1/700 scale in a system that was largely around 1/350, meaning that it would be hard for even a single Epic-scale Terminator to fit inside the model's head. Since most 40K-scale Imperators are based on scaling up the Epic model without realizing it's half the size it should be, they tend to replicate this. Needless to say, the price was correctly scaled to the Imperator's size in the fluff.
Some neckbeards have tried to kitbash a true 1/48 Imperator titan, and found that at 6'10"/2.1m tall, it would just be easier to make a titan costume and stand on the table.
Above assumes you consider Imperator titans on the higher end of the fluff massive scale, the kind of which you see in things like Dawn of War where humans are mere ants crawling around over the top of it. Games Workshop back in the original incarnation of Apocalypse did a 4000 point datasheet for the Imperator Titan which included a scale comparison with a Warhound and a guardsman, where if you built it, it would be almost three feet tall, so on the smaller end.
The size differences given in the fluff are often to do with varying levels of artistic license, as in the older Titan comic books a normal Warlord Titan was absolutely MASSIVE (despite actually saying it stood over 100 feet tall), but when depicted in the Space Marine video game and running around on a slightly smaller Warlord Titan's shoulders it certainly never gave that impression at all. Also, different authors can't make up their minds as to how tall Titans really are, with one Imperator Class Titan (the Dies Irae) being described as both 43 meters tall and 140 meters tall in different novels.
Weaponry
While the classic Epic Imperator had completely fixed armament with no options at all, more recent rules for the Imperator/Warmonger Titan allow it to be armed with a choice of 2 arm weapons and 6 carapace weapons.
Possible arm mounted weapons are the Plasma Annihilator, Hellstorm Cannon, Vengeance Cannon and the Doomstrike Missile Launcher
Possible carapace weapons are the Laser Blaster, Plasma Destructor, Inferno Gun, Vulcan Mega-Bolter, Gatling Blaster, Melta Cannon, Quake Cannon, Volcano Cannon, Apocalypse Missile launcher and the Vortex Missile.