An inference is someone's belief or opinion based only on the information that he/she knows.
"Squatter sovereignty" was a term used by the people that disagreed with the political doctrine which stated that the owners of federal territories should decide if their lands would enter the Union as slave or free states.
The inference being made in the excerpt is the belief that slavery should be allowed inside the territories of people who chose to enslave others, without the interference of anybody else.
