Thankfully, in these tough times there's still plenty of air to go around. Gas may be over thirty bath per liter, but nobody has worked out how to charge for air yet. But why, when air is all around us, does a motorcycle need a special box for the stuff? A box full of air? It wouldn't make a very good sales argument...
And it's such a big item. Most current sportsbikes have replaced the 'fuel-tank' that used to sit under the rider's chin, in front of the seat, with a massive airbox. As example the latest Suzuki GSX-R1000 airbox holds 8.5 liters – that's more than half the size of the fuel tank.
The airbox has a range of small, janitorial tasks to perform – the most obvious one is to hold the air filter. You have to keep grit and dirt out of the engine or it will quickly wear the bores away. Ditto water and small insects and other flying items. A piece of foam or cotton paper will do the job, and as long as the design has enough surface area to flow all the air that the engine needs at peak power, it's all you need.
It also acts as a receptacle for a number of small, noxious outputs: the fuel tank breathers, and finally the crankcase breather pip. This breather in particular contains combustion gases that have leaked past the piston rings along with a mist of hot, stinky engine oil, so it's fed into the inlet tracts. Finally, an airbox will act as a silencer for intake noise, helping the motorcycle pass those pesky noise regulations. These mundane tasks were originally all that the airbox had to do. But when real sportsbikes began to appear in the mid '80s, engine designers realized there were performance gains to be had from a more careful airbox design. Like exhaust systems, a clever airbox can give a broader spread of power from an engine, improve bottom end delivery, and even add 'free' horsepower at the top end.
There are three main ways of doing this. First is by optimizing the air flow into the engine. Hot air is bad for making maximum horsepower since it's less dense than cold air. Less density means fewer oxygen molecules in each liter of air; less gas can be burnt, making less toque and power. So, if an airbox has its inlet at the front of the nosecone rather than right next to the super-hot radiator or red-hot exhaust pipes, it'll get more oxygen in and more power out.
Secondly, if the front-mounted air intakes feed into a sealed airbox you can get a small forced induction effect as the motorcycle goes faster – not unlike a small turbocharger. The incoming air pressurizes the airbox, which crams more oxygen into the engine at each piston stroke, again making more power.
This 'ram-air' effect was first used by Kawasaki on the ZX-11 in the mid '90s, and has since been used on almost every sportsbike produced. The actual power gains are fairly minimal, and only show up at very high speeds. But who cares... they're free. Besides, big frontal air intakes look super-cool.
Lastly, an modern motorcycle airbox can improve power delivery by managing the pressure waves in the intake system. Similar to an exhaust pipe, the engine makes a series of high and low-pressure sound waves as it opens the intake valves into the engine. These waves stream outward from the carburetor or throttle body intake and will bounce off whatever they find. If the intake throats are simply opened to the surrounding air, the waves will be dissipated and not really do anything. But once you add an airbox to the inlet system, you can use the waves to do something more useful. Carefully-sized and designed chambers in the airbox will resonate at certain frequencies, and can actually help improve the airflow into the inlet at certain engine speeds.