it has nothing to do with Mormons, it simply means that America is open to anyone that arrives there, it gives anyone an oportunity to start from scracth and get to the top..from rugs to ritches so to speak, that you are treated just like any other American, born there or not, you have the same rights, but also the same obligations.
Anotherwords, it simply means that the plain is leveled, and it's up to you what you do with this oportuninty.