What's the moment of a force and why would I need to understand it?

Mathematically you'd express it as M=F x d, Moment = Force times distance (from the pivot), unit being Nm, Newtons times meters. Simply speaking, it's how you quantify an object's ability to rotate around it's pivot. Try balancing a pen on your finger, give it a tiny push close to the finger, then at one of the ends, and compare the result - this is because as you apply the force further away from the pivot (center of mass in this case), the moment applied is greater, and so is the "turning ability". We use it every day without thinking about it - have you ever noticed how much harder it is to open a door when pushing on its center rather than the edge, or maybe you were wondering why it's easier to open a jar with a towel on the lid? That's because you take advantage of the increased moment by increasing the force's "arm", or the distance from the pivot. You can use this knowledge, for example, if you can't unscrew a bolt - just extend the spanner's shaft with a pipe thus increasing the force "arm", and the bolt's going to move much easier. You could also try kicking the spanner at the end and at the right angle to the spanner's shaft, this time increasing the Force factor of the equation, although I wouldn't recommend it - this way you can hurt yourself and the bolt. This simple principle is a foundation essential to design multiple objects, from car frames to bridges.