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In North American English,
that is used for retrictive clauses (it restricts the meaning of the noun it modifies), whereas
which is used for non-restrictive clauses (it doesn't restrict the meaning of the noun it modifies). For example,
[1] A suitcase that has no handles is useless.
A restrictive clause is an essential part of the sentence it sits within. Omit it and the sentence changes in meaning:
[2] A suitcase is useless. <Are suitcases really useless?>
A non-restrictive clause is not an essential part of the sentence it sits within. Omit it and the sentence doesn't change in meaning, because
which means
by the way:
[3] The broken suitcase, which (by the way) also has no handles, is useless.
Now, let's omit the non-restrictive clause:
[4] The broken suitcase is useless.
The sentence's core meaning doesn't change.
Does that help so far?
Try here also,
World Wide Words: Which versus that