A common error in English writing.

It's: This is a contraction of "it is" or "it has". The apostrophe is in the place of the missing letter, as is common in English and other languages.

What colour is the cat? It's black.
Where has the cat gone? It's gone out.

Its: This means "belonging to it". This is a possessive pronoun. There is no apostrophe, just as there is no apostrophe in mine, yours, his, hers, ours nor theirs.

What is he doing with the cat? He is brushing its hair.

A stupidly difficult way to remember this follows:

"It's it's if it is. If not it's its."

The easy way to remember is to consider if you really are missing a letter out... if so, use an apostrophe. If not, you don't need one.