Please check my answer

THe cat licked it's paws while the dog watched.

Does this sentence show the apostrophe used crrectly ?

I said yes

http://encarta.msn.com/dictionary_/its.html

it's = contraction (it is)

its = possessive form (owns whatever comes immediately after it in the sentence)

No, your answer is not correct. The sentence "The cat licked it's paws while the dog watched" actually shows incorrect use of the apostrophe. The correct possessive form of "it" does not include an apostrophe. It should be written as "its" without an apostrophe. Therefore, the correct sentence would be: "The cat licked its paws while the dog watched."