What is torque?

is the rotational analogue of force. It is the equivalent of force which makes a body rotate about some axis.
As you may see, it’s the equivalent of force which makes the nut rotate about it’s axis.
Mathematically, Torque, ##tau = r*F*Sin theta##, where ##r## is the length of the rotating arm, ##F## is the force and ##theta## is the angle between the two.
Torque is a vector, i.e. it has a direction associated with it. It is the cross product of vectors ##vec r## and ##vec F##.
Image : hyperphysics.phy-astr.gsu.edu