Identifying adjective clauses are used when we are providing essential, very important information that defines the noun we are describing.
Non-identifying adjective clauses are used when we are providing additional information about the noun we are describing, but it is not used to, for lack of a better word, identify it.
Let me provide some examples, which will make everything clear.
I have two cats. My cat who pees in places other than the litter box remains my cat because she is so damn cute and cuddly.
Note: The adjective clause is necessary to identify which cat is meant. Also note that there is no comma separating the noun from the introduction of the adjective clause. In speech, no pause would be required.
I have two cats. Saku, who is ultra cuddly and affectionate with me, hates everyone else.
Note: The adjective clause is not necessary to identify which cat is meant. Also note that there are commas separating the adjective clause from the rest of the sentence. In speech, there would be a short pause, as required by the insertion of all commas.
One last note:
Do not use THAT to introduce non-identifying adjective clauses. THAT never follows a comma. Instead, use WHO for people and WHICH for places and things.