A background check is NOT just a matter of reviewing your police record. (And BTW, police do not "guarantee" that you have not committed a crime -- only that there is no record of you committing a crime. A subtle difference but still, an important distinction.)
During the background check, they will review the info. that you submitted about your work, where you've lived, gone to school etc. If they have any doubts about the info., they will contact the organizations in question to verify its accuracy. A security background check is also done in conjunction with the Canadian Security Intelligence Service (CSIS). Since CIC needs to confer with other governments, it may take several months for the completion of the background checks.
These checks are used to identify criminals and known security threats (espionage, subversion or terrorism). This is done for every country in which you've lived. They will check things like what organizations you've belonged to, whether you've belonged to the military and any other info. they deem necessary to determine the likeliness that the applicant is a threat to Canadian security.
Since your husband is from a visa-exempt country, he could come here while his PR application is in process. He doesn't have to stay in his country while the background check is in process. However, if they ask him to come to an interview, he would have to return for that.