Work authorization is the legal permission a person has to undertake a particular job in Canada.
Some people need a work permit and some are exempt. Immigration, Refugees and Citizenship Canada distinguishes employer-specific permits, which name the employer and can carry other conditions, from open permits. The useful question in a vacancy is whether the person can do the work offered under their circumstances. A request to confirm eligibility gives no assurance that the employer will support a permit application. Look for any separate wording about that support.
In job listings
OTB Group’s client advisor vacancy in Vancouver required applicants to be legally entitled to work in Canada at the time of application and able to provide proof on request. The listing is asking about permission to take that job, rather than specifying a particular permit for every candidate. Search local jobs for “client advisor”.