There's a fairly regular process where a transitive verb (like know or shoot, which has a subject and an object) can be weakened in its effect by taking the object and rendering it as an oblique argument (in a prepositional phrase) instead. So:
He shot me
Entails that I got hit.
He shot at me
Implies that he missed me.
I know him
Entails that I have met him, that my knowing him is quite strong, whereas:
I know of him
Implies that perhaps I haven't met him, but I have heard of him or that I'm broadly aware of his existence over the grapevine.
In a dictionary, I'd suggest looking for this usage under 'know' rather than under 'of'. It might be there as a phrasal entry. In fact having just looked up the Oxford, I see it as its own subentry under 'know':
To be aware or cognizant of (a person or thing as existing, an event as having occurred, etc.).
And it has the additional information:
Sometimes contrasted with know, as implying little or no knowledge of anything beyond the existence of the person or thing.
As a great example, there was a Simpsons episode in which Bart goes to a new school (because Homer got a job working for an international villain) (source):
4th Grade Teacher: [On Bart's first day in his new school the teacher discovers he can't read cursive handwriting] So, you never learned cursive?
Bart: Well, I know "hell" and "damn" and "get ben..."
4th Grade Teacher: No, no! Cursive handwriting! Script! Do you know multiplication tables? Long division?
Bart: I know of them.