A non-restrictive relative clause is a clause that does not serve to identify or define the antecedent noun, and similar clauses introduced by conjunctions indicating time or place. The sentence is a combination of two statements which could have been made independently.

Here are a few examples:
The dog, which was curious about the cat at first, became uninterested very quickly. 
The children, who were terrifying the cat, stopped terrifying it after it screeched at them.
The executioner who executes his job the best, will get a promotion.

(I could be completely wrong on this.)