As I understand, it's is a conjunction for it is, and its' is an optional use of the apostrophe and it shows a possessive use for its', while its without the apostrophe is the other optional use that also denotes the possessive case.
Writing its' or its can both be used to denote the possessive case because the lack of an apostrophe is understood because it is commonly used without an apostrophe, however its' is more grammatically correct than its without an apostrophe for denoting possession.
Capice! .......... That's Italian for "Understand, do you get it!"
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