BAD : The cat sat in front of the fire, cleaning it's whiskers.
GOOD : The cat sat in front of the fire, cleaning its whiskers.
◆◆◆
it's (WITH an apostrophe) = 'it is' or 'it has': 'It's still raining.' 'It's been raining again.'
its (WITHOUT an apostrophe) = a possessive form like my, his, their, etc: 'The dog has hurt its nose again.'