"Background check" is another one of those terms sometimes used in a specific sense, which as others have described typically is in reference to the the RCMP criminal history check and the CSIS security check, BUT is also used in a more generic sense in respect to the verification and assessment process which is done by IRCC processing agents. The former is often used in the context of WAITING for background check (or background clearances), which is a specific reference to waiting for the RCMP or CSIS clearance or updated clearance.
If there are inquiries or research into open sources, like online media including LinkedIn (mentioned by name because it is an open source which more often pops up in officially published decisions for actual cases), those are ordinarily done by an IRCC processing agent in the local office which is processing the application. This would be part of the "background checks" done in general, IRCC's assessment and verification of the information provided by the applicant. This can range very widely and can include making telephone calls to employers, doing research to verify addresses, telephoning the applicant, including typical Internet searching for information about the applicant.
In addition to the form RCMP and CSIS clearances, there is also the GCMS check. Last we knew this is to be done each time any action is taken on the application. At the least it checks the applicant's GCMS records, verifying identity, client number, PR status, and related information. It can also include cross-checks for residential addresses and employers. Thus, for example, if the applicant reports work history including employment for JakeRivet Company March 2014 to June 2017, IRCC can do a GCMS check to see if there are alerts or information about JakeRivet Company; thus, if JakeRivet Company has been identified in association with a previous case involving fraud, that could trigger further inquiries or even an investigation regarding the applicant's employment with that company.
GCMS also screens FOSS entries, which can include border crossing notes or criminal name-record hits.
The scope of the background check in the broader, more generic sense, can range from minimal to extensive, depending on whether a processing agent sees something raising a concern or question.