Functional requirements are things that the system needs to do, e.g. allow the user to update their address or record their tax details. This often takes the form of User Stories or Use Cases.

Non-functional requirements are often constraints or standards that the system needs to conform to, e.g. which browsers should it work on, what accessibility standards should it meet, how fast should it perform, how many concurrent users should it support, that kind of stuff.

It’s not so much quantitative vs. qualitative, it’s more ‘things to do’ vs ‘standards/measures to meet’.