What are opposing curves?
It is a concept used in creating (drawing, painting, sculpting) organic forms.


  Opposing Curves is no more complex an idea than that curves in nature are rarely if ever related to one another as are parentheses ( ), but that rather they are always offset from / or opposed to one another like the curves in the double helix of a strand of DNA. - from CGSociety


The most simple way to explain this is to say that, when drawing, painting or sculpting organic form, we should never use curves that make the form look symmetrical. Beings are not symmetrical. Objects are. So, to achieve organic form, we should not use curves that make being look symmetrical like the objects are. That is why parentheses are used as an example.



() - symmetrical

(( - Opposing Curves - not symmetrical

)) - Opposing Curves - not symmetrical



If you draw a continuous line with opposing curves, you will notice really nice and smooth flow moving down that line. 

If we look at the human body (or any organic form), we can see many curves but those curves are made of smaller curves. 


  Curves also never curve inward ~ curves are always convex, and never concave. Artists, particularly when they are starting out, draw curves which scoop inward, toward the interior of the form - when in fact, form is created by a series of (sometimes minute) convex curves. - from CGSociety


So, to draw an organic form, lets say a human, we should not use Parentheses () curves to depict the form. 

Example:



I hope I explained it well.

If you would like to know more, you can read this nicely written article I found (link is NSFW, due to artistic nudity presented): http://www.cgsociety.org/index.php/CGSFeatures/CGSFeatureSpecial/opposing_curves