It's always means "it is." If you don't mean "it is," then don't use "it's." It's an exception to the possessive -s- rule.
I disagree with "its" here because it's considered distasteful to use "it" for a living being. In the US, we would more often now use his, her, or their (as an un-gendered singular pronoun): The dog drinks his water. The dog drinks her water. The dog drinks their water.
"sin" indicates something owned by the subject itself, whereas "hennes" indicates something owned by a female that's not the subject.
For example, you and your friends are out for a run. Your friend (James) asks where your other friend (Sandy) got the water she's drinking from. You know that your 3rd friend (Caroline) brought it, so you say, while pointing at Caroline "Hun drikker vannet hennes".
I hope this (kinda complicated) explanation helped.