While an Airship is generically a lighter-than-air vehicle for airborne transport, those found in the world of Girl Genius are far more than such simple craft.
Airships are the primary mode of aerial transportation, and so dominant that when Gil shows Agatha his (or, as he'd probably prefer to think of it, his flyer), it's the only heavier-than-air flying machine that we'll see for quite some time.
Furthermore, in a world where those in power would rather build piston-leg vehicles than maintain roads, and rail transit is the domain of religious fanatics, airships are an overall primary means of transportation for those who can afford them.
In the world of Girl Genius, airships work.
Airships serve not only as transports but also, of course, as weapons systems. In addition to the ones bearing guns for air-to-air combat (which is to say, most of them), Klaus maintains a fleet of "bomber" airships for both suppression and containment missions. He gets ... distracted ... before he gets to use them in this , which is just as well.
In general, airships are Really Cool, and there is much more to be said about them.
The great-grandpappy of all airships is Castle Wulfenbach; needless to say, most airships aren't nearly as big as this behemoth. In all likelihood, if someone tried to build a bigger one, the Baron would instantly destroy it, and likely the builder along with it.
The "Pink Airship"
However, while Castle Wulfenbach is probably the largest airship out there, it's not the most modern one. An important plot point is that when Zola "Heterodyne" on Mechanicsburg to try to take control of Castle Heterodyne, she leaves a brand-new, modern airship overhead for insurance, and also as a viewing platform for some of the powers behind her. Some nice, if laid-back, by Vanamonde von Mekkhan reveals that this shocking pink apparition is "a flash ship, a new type out of the Stockholm yards." We don't know yet how this new-fangled, if garish, design improves on older ones; stay tuned.
The Foglios named the publishing branch of Studio Foglio, LLC "Airship Entertainment".
It might be noted that although there are a number of technical difficulties with lighter-than-air vehicles which have prevented them from wide usage in our world (and a number of theories have been proposed as to how they have been overcome in Girl Genius), none are insurmountable save two - public opinion and subsidization. Several tragic accidents -- such as using a doping formulation that is basically solid rocket fuel to seal the Hindenburg's envelope fabric, and weak engines that were unable to avoid storms -- have soured the common view of airships. Second, airships have significantly less military capability than aircraft - all real life aircraft are subsidized for military applications, and this support is denied to airships. However, research continues even today, as the availability of helium and powerful engines make them much safer - and due to the mathematical fact that volume to surface area (which is to say, lift vs. cost) ratios increase with scale, a megascale airship such as Castle Wulfenbach is more efficient than any given smaller one.
Additionally, airships are making something of a comeback. This one, the P-791 by Lockheed, is especially interesting. It may well use Ultra High Molecular Weight Polyethylene, as its primary material of construction and therefore relies on vacuum tanks for buoyancy instead of flexible bags full of helium. This, along with its shape provides the lift it requires for flight. Its engines are mounted on gimbals for steering and pitch control. These recent developments eliminate all the major obstacles to passenger airship operations, save that of building suitable hangers for them.