A couple is a pair of equal, opposite, parallel forces that produce pure rotation

Moments, Couples & Equilibrium — AQA A-Level Physics

Key Definition

Couple — A pair of equal and opposite coplanar forces whose lines of action do not coincide, producing rotation only with no resultant linear force.

$$\tau = Fd$$

The forces must be equal in magnitude, opposite in direction, and separated by a perpendicular distance.
Because the forces are equal and opposite, the resultant force is zero -- the object does not accelerate linearly (Newton's second lawThe resultant force on an object is equal to its rate of change of momentum. For constant mass, F = ma.).
The moment of a coupleA pair of equal and opposite forces whose lines of action do not coincide, producing a pure turning effect (torque) with no resultant force. does not depend on the position of the pivot.
Moment of a $coupleA pair of equal and opposite forces whose lines of action do not coincide, producing a pure turning effect (torque) with no resultant force. = Force times perpendicular distance between$ the lines of action of the forces.

M = F \times d

$M$: moment of the coupleA pair of equal and opposite forces whose lines of action do not coincide, producing a pure turning effect (torque) with no resultant force. (N m)
$F$: one of the equal forces (N)
$d$: perpendicular distance between the lines of action (m)

Common Mistake MEDIUM

Students often: Don't say two forces in the same direction form a couple.
Instead: A couple requires equal forces in opposite directions. Same-direction forces cannot produce pure rotation.

Examiner Tips and Tricks

The forces that make up a couple cannot share the same line of action.
If both forces act along the same line, they either cancel (no effect) or add (translation, not rotation).

Related:Newton's Laws