BHP = Brake horse power. It says that it is brake horse power but it is generally relates with high pick up (your bikes reaches top speed in lesser time). So what does this actually mean?.
Torque = vertical distance x FsinΘ , how is that related to bikes and how does it affect performance?
Torque is how strong your engine is and Horsepower is a measure of how fast it can use that power.
That is why a Diesel engine with 400Nm of Torque cannot out-accellerate a petrol car with 400Nm of Torque. Horsepower is calculated by multiplying the amount of torque by the RPM of the engine (and dividing by 5,252. But that's not important here). Because a Diesel produces its power at say 2000 RPM, it's BHP figure would be rated at 152BHP, meaning that although it's a very strong engine, it cannot use that power very quickly. The petrol engine makes 400Nm at 6000RPM so the formula gives us 456BHP.
Both cars can pull a fair amount of weight, but only the petrol engined car can do so quickly.
I don't know anything about bikes or what is considered a "strong and quick" bike engine, but the facts remain the same.
I should probably add that Break Horsepower (BHP) is measured at the flywheel, while Horsepower (HP) is measured at the wheels.
Torque in a motorcycle
The piston moves up and down, and the force for that comes from the fuel that is burned. Connected to the piston is a rod, the connecting rod, and that rod is connected (with the ability to turn) to the crankshaft.
The distance between the pedal to the rotation point is comparable to the distance between the crank and the middle point of the crankshaft, and in the same way as in the bicycle example, the distance "counts" for 100% when the point of the crank that is connected to the rod has an angle of 90 degrees with the direction of the piston, and for 0% when that point is in the highest or the lowest position.
Maximum torque A piston, therefore, delivers a varying amount of torque. The torque at a certain rpm is the average torque that the piston delivers during the revolution stroke. And when your motorcycle has more than one cylinder, the torque of the individual pistons add up.
The rpm where the maximum torque is delivered, is the rpm where the fuel is burned most efficiently: it is at that rpm that the piston delivers the maximum torque on the crank.
The gearbox transmits the rotation of the crank onto (ultimately) the wheels.
What does power (BHP) mean?
The amount of power tells how fast work can be done. When you walk up the stairs for instance, you deliver work, carrying your own weight up the stairs. How fast you can do that determines your power (in combination with the length of the stairs and your weight: they determine the amount of work).
Power is expressed in kilowatt (Kw) or in Horsepower (Hp).
When you know the torque of your motorcycle with a given rpm, you can deduce the power, by multiplying the torque with the number of revolutions per minute (and of course with a constant factor to adjust the different dimensions like rpm, Hp and Nm).
From Wikipedia:
Brake horsepower (bhp) is the measure of an engine's horsepower before the loss in power caused by the gearbox, alternator, differential, water pump, and other auxiliary components such as power steering pump, muffled exhaust system, etc. Brake refers to a device which was used to load an engine and hold it at a desired rotational speed. During testing, the output torque and rotational speed were measured to determine the brake horsepower. Horsepower was originally measured and calculated by use of the "indicator" (a James Watt invention of the late 18th century), and later by means of a De Prony brake connected to the engine's output shaft.
In the US, car's HP is rated at SAE net so as to give a truer value of HP available at the crankshaft. SAE net is the HP output of the engine after the alternator, waterpump, power steering, etc., are added to the vehicle. Automotive manufacturers used to use SAE gross, which is BHP equivalent. This gave a misrepresentation of what the owner could expect from the vehicle as far as performance. This all came about during the HP wars of the 60's and 70's.
EDIT: (realized I didn't answer the second part of your question)
Also, from Wikipedia:
Torque, moment or moment of force, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist to an object. Mathematically, torque is defined as the cross product of the lever-arm distance and force, which tends to produce rotation.
In the automotive world (or bike world in your case), torque is the force which gets your bike moving. The more torque, the quicker the bike can move. You will usually hear two different terms: torque and horsepower. Torque is the twisting force; mechanical horsepower is a number derived from the equation
Where -
HP is usually considered the force which keeps the vehicle moving and is the rate at which work is done.
BHP(Brake Horse Power) is the common rating that we consider while measuring the power of a bike. Technically it is the maximum power produced before it is delivered to the drive train. Torque is the turning effect produced by the engine. Peak Torque is available in lower RPM's. The naive categorization is :
In lower gears we get more torque. In higher gears torque decreases and power increases. When go uphill we require torque. HP is the other way. But an engine has different sweet points(RPM's). The one where it gains maximum power and the other where it gains maximum torque.
Torque is a turning moment. In an engine this moment is available at it's flywheel. Brake Horse power is the rate at which torque is applied.
An increase in engine speed implies a decrease in torque.
The faster your engine turns from rest, the greater the torque is applied, and so has greater HP. This applies only up to a point. As engine speed increases the torque will begin to drop off. Its HP output will become less efficient with further speed increases.
For most road going vehicles torque begins to drop off at around 2000 rpm, but HP at 3500 rpm. These fiqures can be manipulated by engine design according to what service the engine will be put to.
