She talked about the people and things she's interested in.

Literal

She [topic-は] interest [subject-が]-existing people and things [about-について] talk [object-を] did.

関心のある is the attributive (pre-noun) form of 関心がある ('to have interest in') — when an existential ある-clause moves inside a noun-modifying position, the が often softens to の (the 'noun-modifying の'). So 関心のある人々 means 'people that interest [her].' 人々や物事 stacks two nouns with や ('and others'), the listing particle that implies the list is non-exhaustive — 'people and things and so on' — softer than と, which would suggest a complete enumeration. Finally ~について ('about / regarding') is the standard topic-marker for what speech, writing, or thought is concerning. 話をする is the noun-plus-suru pattern for 'have a conversation,' framing the talk as a discrete event.