The phrase "to know a quality" means to have a deep understanding or familiarity with a specific attribute or characteristic of something. Full definition
This gives you peace of mind knowing your quality of living will always be preserved. (himpro.ca)
We don't know the quality of the other two - thirds — the schools that never start — but we do know something about why they don't make it. (educationnext.org)
Finding a real gem in your average drugstore makes you feel savvy, like you really know quality when you see it and definitely don't care about name brands or trends. (manrepeller.com)