Motorcycle brakes have been accelerating, at least in terms of their technology, in the last decade, growing pistons, sprouting new mounting systems, and gaining power assistance. Even some cast-in-steel certainties you could always depend on, like disc being round, having started to look wavy.
The impressive reductions in mass of most manufacturers' motorcycles in the last few years might have taken some pressure off that brakes have to cope with, if only riders weren't busy getting fatter and spoiling it, but the main forces driving the advance are improvements in tire technology and increasing top speeds. More grip from road rubber, pioneered by more grip being found in race tires, means brakes have to be stronger to be able to exploit it, and they need to do so in a manner that is as easy-to-control as possible if they're to be any use.
Higher top speeds (and on MotoGP motorcycles we're talking in terms of 320km/h plus regularly, or more precisely, while many road bikes are capable of a least 290km/h) carry a double whammy, or more precisely, a whammy squared. A brake's job, at its most fundamental level, is to convert your kinetic energy, the energy you have due to your speed, into heat. The faster it does that, the more rapidly you slow down. What makes its job so demanding is that your kinetic energy increases in proportion to the square of your speed, so a motorcycle at 160km/h has accrued four times the kinetic energy it had at 80km/h. It's not quite true to say the brake therefore has to shed exactly four times as much heat at twice the speed because wind resistance for once is on your side. This also increases with the square of you speed so it's trying four times harder to slow you down at 180km/h as a 80km/h, and the brakes get a bit of help. But not enough to make a big difference – the square of your speed is the dominant factor, and you can be sure that the kinetic energy of a fully fueled Suzuki Hayabusa with a average Thai rider at 310km/h has to be converted into an awful lot of heat to lose though the brakes when it's slowing to a standstill. Try sticking your tongue on the discs straight afterward and hear how loud it hisses. You can do this in the dark if you like as they'll be a glowing-red-hot 800c degree. Even in normal road use they can get up to 400c degree, so if you value your taste buds disc-licking is probably best restricted to before you set off.
You don't have to use the brakes; you could coast to a stop from 310km/h Eventually... But the same amount of energy would still have to be lost, which happens as heat in the tires and bearings, a small fraction as noise, and kinetic energy given away to the air, as the turbulence you cause. It just takes longer. What brakes do is shortcut the process, grabbing big buckets of your kinetic energy and spitting it out as heat as fast as they can, depending on how hard you're pulling the lever.
And that's the bit that matters, what happens when you pull the lever. Years ago this would usually operate two shoes inside a drum via a cable, but drum brakes are limited because the heat is generated inside the wheel, away from the cooling airflow, and the length and curve of brake shoes means very high pressure can't be applied without distorting them. So disc brakes were invented. The friction surface where the heat is generated is out in the open, the disc and caliper are simpler lumps of metal which suffer less from heat distortion, and because brake pads are small, chunky, square-ish things, much higher pressure can be applied to them than shoes, resulting in an increase in friction and braking force.
In all but a handful of cable-operated oddities, those forces are applied by hydraulics, a very useful way of translating and magnifying a force from somewhere convenient to somewhere awkward and mobile, like from a handlebar to a caliper on a bouncing fork leg.
The advantage starts when you squeeze the brake lever, as this gives you immediate, er, leverage, over the brake's master-cylinder of about four to one. Move the lever 20mm where you´re squeezing it and it pushes a piston into the master cylinder by 5mm, but with a four times larger force than you're applying. If that piston has a 10mm diameter, it displaces about 0.4cc of brake fluid into the brake hoses. The fluid doesn't compress and decent hoses won't expand significantly, so at the other end 0.4cc is displaced into the only place it can go, behind the piston in the caliper that pushes the brake pad against the disc. Let's say this piston has a 40mm diameter, in which case it only needs to slide forward 0.31mm to accommodate this extra 0.4cc.
In other words, 5mm movement of the piston at one end produces just 0.31mm of movement at the other, 16 times less movement but with 16 times more force, and if you now factor in your brake lever gains you've turned 20mm finger movement into 0.31mm piston movement and multiplied the force a further four times, a total of 64 times. You have the power.
The small amount of movement of the caliper piston is not a problem as brake pads are brushing against a disc's surface anyway, so the consequence is the pads can be squeezed against the disc with colossal force, the friction rises dramatically, loads of heat is generated and the motorcycle slows down.
This is the underlying principle, what comes next is refining it to make it work more effectively and this is where, compromises come into play. The first and most obvious is that calipers and discs add weight to exactly the area where it's least wanted, the unsprung mass of a wheel assembly and suspension. More mass here adversely affects ride quality and grip, and worse still, brake discs add gyroscopic effects which slow steering speed, as well as increasing the rotational inertia of a wheel. And ironically, that impairs braking as well as acceleration.
This is decision time when specifying the disc diameter. A larger diameter disc will increase your braking power for simple leverage reasons that you'll understand if you image trying to stop a spinning cycle wheel. Grab it a the tire, a long way from the axle, you have plenty of leverage and it's relatively easy to stop. Now try to stop it by grabbing the spokes near the hub, and you'll struggle as you don't have much leverage. In the same way,large diameter discs mean more braking power, but as they're bigger they also weigh more and increase the gyroscopic forces because of their increased diameter. The first compromise then is between stopping power and other chassis requirements.
You can make the disc thinner and shed some weight that way, but thinner discs are more prone to distorting and permanently warping with heat. They also need to cope with some very large forces, so you don't want them so thin that they break or crack when used in anger.
Another solution is to make the disc narrower when viewed from the side, so is inner diameter is closer to its outer diameter. The disc becomes usefully lighter, but the problem is you would have to make the brake pads smaller, reducing friction and negating any other gains. The answer here is to make the brake pads londer and thinner to maintain the total area of contact with the disc. But brake caliper pistons have to be round to maintain an even pressure across the pad, the solution is to have two pistons operating on the one pad, one at each end. And now, with a pad and two pistons on each side of the disc, you have a four piston caliper, as used on most self-respecting sportsbikes.