Yeah, it absolutely is vague. I had reason to read some GDPR stuff a while back - that phrasing is just lifted from there. Article 6 is about what reasons you could have to store private info. 1f is, apparently... yeah, you're just "legitimately" interested. Wonder what that means? So do I.
(f) processing is necessary for the purposes of the legitimate interests pursued by the controller or by a third party, except where such interests are overridden by the interests or fundamental rights and freedoms of the data subject which require protection of personal data, in particular where the data subject is a child. (Point (f) of the first subparagraph shall not apply to processing carried out by public authorities in the performance of their tasks.)