The national Monument Foundation says:

Where on the Statue are the broken chains located, and what do the chains mean? The broken chains are near the Statue's feet, and are not visible from the ground level. Many believe that the chains represent breaking free from tyranny and servitude.

Which makes sense, but rewriters of history claim it was for the slaves. The architect wanted chains on the statues hands, but American financiers refused to support the project if he did.

There's a lot on the subject, but I think it has more to do with Freedom and a Nation breaking away from English Tyranny.