Here's how it works:
Example: immigration statistics site:.gov
This will only bring you results from sites with the .gov domain in the url
immigration statistics site:dhs.gov - limits search to Department of Homeland Security websites
immigration statistics site:census.gov - limits search to Census Bureau websites
immigration statistics site:justice.gov - limits search to Department of Justice websites
Why would you want to search government websites?
The US Government is a huge publisher of technical, statistical, scientific and cultural reports. There is a wealth of information on a huge range of topics from all sorts of government agencies and, by law, information published by the US Government is free!