A 'moment' is a force that tries to bend the structure to which it applies. When you pull (or push) on a wrench you're actually imposing a bending moment in the wrench. Think of a torque wrench  you pull on it with a force of, say 20 lbs, and the wrench is, for example, a foot long, you're applying a bending moment of 20x12 or 140 inchlbs to the handle of the wrench, which results in a torque of 140 inchlbs to the bolt or nut the wrench is attached to.
Another example: walking out on a diving board. If you weigh 100 lbs (well, not you specifically, just an example), when you first stand on the fixed end of the board you're exerting a force of 100 lbs on the board, but no bending moment as you are directly over the fixed end. As you walk out on the board your weight doesn't change, so the force you exert on the board doesn't change, but the board starts to bend. What's happening is that as you move away from that fixed end you are exerting two forces, one being your weight and the other being a bending moment that is the product of your weight times the distance you've walked away from the fixed end. Both forces cause stress in the board and both must be considered in any structural analysis.
