In short, functional requirements are functional features which are expected by users from a proposed software product. Non-functional requirements on the other hand are more related to security, performance, and the look and feel of the user interface, a.k.a. (UI). In order for a project to be successful, it is critically essential that both the customer and the project delivery teams have a clear definition and agreement on what the project scope and detailed requirements are going to be.

There are three types of requirements: conscious, unconscious and unidentified or TBD requirements.
When a hiring manager asks this question, they want to know if part of your job requires gathering and analyzing functional or non-functional requirements. For functional requirements gathering, they will want to hear things like how the system behaves under certain conditions within its environment, how it responds to inputs and what outputs it generates. As far as non-functional requirements, they will want to also hear things like constraints on the system, quality attributes, security, performance and availability for example.