Torque is the rotational equivalent of force.
To get an object to move in a straight-line, or to deflect a moving object, apply a force. Similarly, to get something to spin, or to alter the rotation of a spinning object, apply a torque.
If you understand how to open a door, you understand something about torque. To open a door, where do you push? If you exert a force at the hinge, the door will not move; the easiest way to open a door is to exert a force as far from the hinge as possible, and to push or pull with a force perpendicular to the door. This maximizes the torque you exert.
The magnitude of the torque depends on the force, the direction of the force, and where the force is applied.
τ = r × F
The magnitude of the resultant vector is r F sin(θ). r is measured from the axis of rotation to the line of the force, and θ is the angle between r and F.
The direction of the torque is given by the right-hand rule. Using your right hand, point your fingers in the direction of the first vector (r) and curl them into the direction of the second vector (F). Your thumb, sticking out, will point in the direction of the torque.
The torque is ...