What causes "stringy" melted cheese (and similar behavior in other materials)?
When cheese is heated to 140 degrees fahrenheit, the proteins line up in rows.  Soaking the cheese in a salt solution before pulling it helps to stiffen it and keep it pliable, as the salt neutralizes acids which could cause the long lines of protein to break.

Polymers, similar to cheese, can be stringy because their molecules are very large (macromolecules), and tend to entangle with one another.  @IanF1 is correct in saying this may be a chemistry question.  Here is a good explanation of polymerization:

http://courses.chem.psu.edu/chem112/materials/polymers.html