These days, which and that are often used interchangeably without causing any ambiguity. However, prescriptive grammar distinguishes between their usages.
In prescriptive grammar, which introduces a clause that adds extra information to a sentence. Such clauses are called non-restrictive or non-defining clauses because you could delete them and the rest of the sentence would still make sense.
Non-restrictive clauses need to be separated from the main idea with commas, dashes or brackets.
The bag, which I bought yesterday, broke today.
The bag – which I bought yesterday – broke today.
The bag (which I bought yesterday) broke today.
That defines the main idea and introduces a clause that is called a restrictive or defining clause. You can often delete that in these clauses without any loss of meaning.
This is the house that Jack built.
This is the house Jack built.
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