A race airbox is a larger volume airbox which does away with the air filter (or uses a minimal one) and normally encloses the carbs, i.e. the carbs sit inside the airbox.
The reason people sometimes use them is that they have a larger capacity and flow more air allowing you to tune the engine for more HP. They also make it easier to get to the carbs (as they just sit inside the airbox). On ram air bikes, the fact that the carbs sit inside the airbox removes the need for the “Float bowl” mod as, with this arrangement, the bowls are already properly pressurised.
There are usually two types of race airboxes. The ones that have their own lid and those that use the fuel tank as the lid. The latter have the advantage of more volume, but can be hard to get a good seal with the tank.
Many manufacturers offer race airboxes, but don’t expect them to come ready for you to fit. Buying one is only the first step. Often it is left up to you to cut the holes in the bottom of the airbox to mate it to the inlet manifolds. These airboxes normally come with no seals so getting them to make a good seal is a DIY job! Best materials for these are foams of various density, but if they come into contact with the engine make sure that they can stand the heat.
As far as I am aware most race airboxes require you to remove the “fresh air induction system” (as Kawasaki calls it) as this usually ends up in the way of the air intake of the new box. This is the assembly of hoses that connects to the top of the cam cover. You then need to block the holes (not too difficult with some ingenuity although in my case I didn’t need to as I use a Racekit cam cover without those holes already)
Another point worth noting is that most of these airboxes are tailored to fit racing FCR carbs. I am not sure how well the CV carbs of J, L and P models will fit (although I am sure that they can be made to fit if you are prepared to work for it), but I can tell you that the FCRs that come stock with K,M and N models don’t usually fit perfectly because the float bowl of these carbs is different from the aftermarket ones and requires more space whilst most of these airboxes only allow for the shorter racekit float bowls. The cheap option here, if the carbs don’t fit, is to modify the airbox with some fiberglass.
It is also a good idea to make up some sort of airfilter. It doesn’t have to be as thick as the stock one, just as long as you are prepared to clean it more often. Having said that finding a good way to fit a filter can also be challenging.
For ’91-’95 models fitting a race airbox often also involves lowering the radiator by about 5cm to allow for the ram air scoop that these boxes usually have (though some 93-95 boxes use the stock intake only without the additional one over the rad). Don’t expect the lowering brackets to be included in the kit. You’ll have to make these, but it is simple enough.
Also see the piece about fitting a Race Airbox to a ZXR750R-K. Although this is model specific outlines many issues and solutions that are common to all models.
Here are a few links to Race Airbox manufacturers/retailers