The concept of a moment (or force moment) is that of a force at a distance. It not only measures how strong the force is but also how far away it is applied (for rotational purposes).
Consider s see-saw with a bear and a skunk.
In order to quantify the idea of "balance" you need a description of the weight of each object as well as how far away does this weight apply relative to the fulcrum (red triangle).
You equate the moments
$$ \mbox{moment of bear} = \mbox{moment of skunk} $$ $$ x_B\, W_B = x_K\, W_K $$
where $x_B$ and $x_K$ are the distances (of the bear and the skunk respectively), and $W_B$ and $W_K$ the weights (of the bear and the skunk respectively).
The units are $\mbox{[length]} \times \mbox{[distance]} $ for moments. In the SI sytem that is $\rm N\,m$ (Newton-meters) and in the customary units $\rm lbs\;ft$ (Foot-pounds).