La Liberté éclairant le monde (Liberty Enlightening the World) is a gift from the people of France to the U.S.A. to recognize what the French saw as their co-developers of national liberty.

The statue is of a robed female figure representing Libertas, the Roman goddess of freedom, who bears a torch and a tabula ansata (a tablet evoking the law) upon which is inscribed the date of the American Declaration of Independence, July 4, 1776. A broken chain lies at her feet. [Wikipedia]

Symbolizing abolition.

It didn't have much to do with immigration. The message to the world was that America and France had liberated their own countries and you should admire this statue, then be inspired to go home and liberate your own country.