How are Belgian fries different than the average French fries found in North America?
All of the sources I read say the same thing... what makes them different is that they're fried twice.

From Saveur:


  Frites are the supercharged cousin to paltry American-style fries: made from soft Belgian potatoes called bintjes, they're thick-cut and—this is key—double-fried (in the olden days, in molten horse or ox fat, though modern options range from lard to vegetable oil). Served in a paper cone with mayo and ketchup, properly executed frites—the ones that have been fried, dried, then carefully fried again—are an addictive riot of textures: soft and fluffy on the inside, surrounded by a crunchy, greaseless crust, dipped in luxuriously flavorful sauces.


From Epicurious:


  There is no fancy skill involved in making these crispy fries, but there is a trick. The potatoes are fried twice. The first time cooks them through and makes them tender. The second time, which can be done hours later just before serving, turns them golden brown and deliciously crisp.


From a site dedicated to the Belgian Fry:


  So high time time for a (simple) definition of what makes fries Belgian Fries: 
  
  
  freshly cut, irregularly shaped  
  cooked (fried) twice
  fluffy on the inside, crispy on the outside
  a distinct potato taste
  at least 10 mm thick
  preferably served in a paper cone
  


Some sites mention the importance of certain fats or types of potato but the one similarity for all sites is the fact that they're double fried.