The language acquisition device is a specific language "organ" in the brain that Noam Chomsky hypothesized humans possess. Since children say things like "foots" instead of "feet" and "goed" instead of "went" even though they've most likely never heard these terms before implied to Chomsky that children follow syntactic rules in their heads rather than just imitating what they hear.
Here's a short video of Chomsky himself explaining this idea:
Think of it this way, your parents probably never taught you specifically to add an 's' at the end of a word to make it plural, or an 'ed' to make it past tense, it's something you picked up on our own. Chomsky's theory says this is because we're biologically inclined to know and pick up on syntactic rules rather than having to be specifically taught them.
This theory is important to nativists because it gives evidence to their belief that children are born with some basic knowledge of how language work.
I would like to look more in to studies done on the language acquisition device, to see if there's more evidence showing that syntactic rules are something we're born with and if there are other parts of language that we could possibly be born with rather than having to learn.