“Act on” means they (the legislators) were forced to something about it (the hostility).
“Usher in” means, more-or-less, “began”. So, “…began the biggest crackdown…”
“Crackdown” means, mostly, “to put a stop to it.”
“Spur” means “to incite” or “aggressively caused by”
“Spark” means “to ignite” or “to start”
“Wave” means what you would think it does; like a “wave of water” washes over you physically or literally in the ocean, but instead a “wave of laws” washes over you mentally or figuratively in court.
And finally, “to address” means “to deal with” or sort of, “to look at/to consider”
An easier version of your passage would look something like:
“Legislators decided to deal with that hostility, beginning to put a stop to unlawful immigrants for the first time in decades. Since 2006, the record numbers of unlawful immigrants arriving, coupled with the hostility brought on by a recession, started a large group of local and state laws aimed at handling unlawful immigration.”
My version is definitely not perfect, but hopefully it helped you understand the passage a little bit more!