The concept of torque is a fundamental quantity, defined by the rotational power divided by rotational rate.  Rotational rate is 2 pi (one revolution) times the rotational speed.  Of course, with other than coherent units, a conversion factor may be necessary to find the torque.
 
Depending on the equipment involved, torque can be different at different points in the equipment.  Speed reduction devices, such as gear reducers, belt drives, etc., are essentially constant power devices, but have the ability to reduce rotational speed, which is in the denominator of the torque calculation.  Same power, lower speed, higher torque.
 
For example coming out of an electric motor, you know the power of the motor (hp or kW) and the rotational speed, such as 1,800 rpm or 1,500 rpm, depending on the frequency of the power supply.  Putting the calculation in coherent units eliminates the need for a conversion factor.  So torque (in Newton meters) is power (in watts) divided by 2 pi (2x3.14159) times the rotational speed (in revolutions per second).  At the output from a gear reducer on the same piece of equipment, the torque will be multiplied by whatever factor the speed is reduced.  For instance, a 5:1 gear reduction will increase the motor torque by a factor of 5.
 
In general, power remains constant (otherwise heat must be dissipated) and torque increases as speed is reduced.  I hope this explanation answers your question.