The Moment of Force or Torque is the measurement of force applied to a body in such a way that the body is subjected to rotational change in its position. This is one definition of "moment" in physics, which can apply to several different measurements. In this case, the effect of force on an object causes it to rotate around an axis, either real or simply based on its inertial state (moving or static), and it is usually differentiated from simple pushing or pulling forces.
The full mathematics of torque or moment of force depends on many different variables, and requires a working knowledge of mechanical math and physics, but the basic principle is: force applied to an object tends to rotate it around an axis, and is measured by the amount of force multiplied by the distance of the force from the center of the affected object.
Adrian Roberts comments that while length and distance of an object can be objectively measured, the only thing that can be measured of force is its effect on an object.
...the moment of the force... is equal to the magnitude of the force multiplied by the perpendicular distance from the point about which the turning effect is being measured.
(Roberts, Statics and Dynamics with Background Mathematics, Google Books)
In simpler terms, measurement is the power of the force multiplied by its direct-line distance from the turning point. For example, turning a wrench on a nut would multiply the force used on the wrench by the length of the wrench to the center of the bolt (not the nut, since the nut is rotating around the bolt).