What is the difference between the speed and the torque of a motor?

1. An good answer has been provided by Michael Williams. I will try to add in a few points. 

Speed (angular velocity) of the motor is measured in the number of rotations per minute (RPM) or radians/second. It is the number of times the motor shaft has turned during a given time period. 

Torque can be called rotational force. It is the force that the motor has to develop to rotate an object. 

The power consumed by the motor is the product of the torque and the angular velocity. Hence theoretically, when the power remains constant, if the load that the motor has to turn increase, its speed will decrease. 

When a force F acts on a body of Mass then the acceleration produced is given by Newton's law.
           F = M*a,        where a is the acceleration.
And when a Torque T is applied on a body having a Moment of Inertia, I about the point of rotation, then
          T = I*a,          where a is the angular acceleration. 
Compare the two equations. That is why torque can be called rotational force.

2. Let us assume that two cyclist are riding. The first cyclist is riding alone. The second cyclist is riding with an additional rider at his back. Let us assume that both are travelling at the same speed. But, both of them will not exert the same force. i.e., the first cyclist exerts less torque and the second one exerts more torque, though both are travelling at the same speed.

For a motor, speed is measured in revolutions per minute. Torque is force exerted as an object rotates. To turn a motor shaft requires a certain amount of torque. ... An eight cylinder car engine can run at 3600 RPM and exert a great amount of torque

3. Speed is a measure of how far something travels in a given period of time. The rate of change in position. For a motor, speed is measured in revolutions per minute.

Torque is force exerted as an object rotates. To turn a motor shaft requires a certain amount of torque. If a load is added to the shaft, more torque is required to turn it.

Two motors of different sizes may run at the same speed. A shaded-pole motor (example: window fan) exerts very little torque. A common speed is 1800 or 1200 RPM.

A large industrial motor (example; factory conveyor belt) may exert a very high torque in order to start a heavy load, and yet it runs at a similar speed.

The same is true of engines. An eight cylinder car engine can run at 3600 RPM and exert a great amount of torque. A small generator will run at 3600 RPM, but not exert nearly as much torque as the car.

• Power: The Power produced by any engine is the capacity of that engine to take the motorcycle to its maximum speed.
• Torque: The Torque generated by an engine is an entity which determines the pulling capacity of the bike or any type of engine.

The definition given above, the more the power of your bike's engine has the more speed it gets. That means if your bike has Top Speed of 120 Kmph with 17 Ps of power, if somehow the power of your bike increases it will be able to achieve higher Top speed than before. Generally the petrol engines which are also called as "Suicidal in nature" extract the peak power at higher Rpms, as you go higher on the power band it will start coming out at higher Rpms given the other factors remaining same.

the Torque you need to remember that we had defined the Torque as an entity which is responsible for the rate with which your bike pulls you. In simpler term while Power is related to the "Top Speed" of the bike the Torque is related to the "Acceleration". The more Torque your bike's engine generates the more quickly your bike accelerates.