A quality system is a system of processes and procedures that an organization implements to describe how the company addresses Design Controls requirements and other medical device regulations.
The FDA enforces to establish a quality system under 21 CFR Part 820, which you must follow if you are planning to go to market in the USA.
In Europe, it requires establishing a quality system to meet the medical device guidelines either under ISO 13485 or EN ISO 13485. For Canada, it validates quality system certified by ISO 13485.
FDA 21 CFR Part 820 and ISO 13485 are similar, which means you can establish a quality system that fills requirements for the USA, Canada, and Europe.