Topology; What is it?

I'm finding it really hard to describe topology as everyone uses different methods to map out the face and it's key elements.  It's simply mapping out the face and its features and how its seen, this uses certain patterns and loops of the face, I found this picture [1] somewhat helpful and mapping out the loops on a face; 

Here is what i have done to Kai's face, my model, using topology;  

This is the best I can explain topology as when I try and research it I cannot find most websites useful other than finding what people feel is the best method to use. 

[1] http://www.google.co.uk/imgres?q=topology+in+faces&um=1&hl=en&safe=off&sa=N&biw=1920&bih=955&tbm=isch&tbnid=2h5VHXSrflKE-M:&imgrefurl=http://www.digitaltutors.com/forum/showthread.php%3F9365-human-face-topology&docid=Vchp0rZ4NH6_HM&imgurl=http://i9.photobucket.com/albums/a84/Monkey_Knife_Fight/EdgeLoop1.jpg&w=1167&h=850&ei=krBKT92hEKmg0QXpsamvDg&zoom=1