What does "Passed out of record" mean?

There is a contrast between passed out of record and into renown.

For "passed out of record", imagine a set of logbooks for keeping records. First, a person is born, then they become a parent, then a grandparent, then a great grandparent, and so on. All this is recorded. Eventually, it becomes too much of a hassle to keep updating the old records. There isn't enough space to keep every logbook, so the old ones get thrown out. At some point, the oldies aren't mentioned anywhere in the extant logbooks - they have passed out of record.

This contrasts poetically with "into renown", but that discussion would be pressing against the boundaries of EL&U.

In this context, I would say passed is being used in the sense of meaning 'transition'

From Merriam-Webster:

5. to go from one quality, state, or form to another

https://www.merriam-webster.com/dictionary/passed

So they transitioned from simply being part of a record, or part of history, into the renown or legendary status.