is there a commonly-agreed-on definition of what this means?
Generally, good peer-review means that experts in your field carefully read your work and evaluate its merit. The definitions of "experts" and "carefully" vary widely across disciplines. Some fields require several rounds of meticulous back-and-forth between author and journal; others are less stringent.
Is there a publicly verifiable process to verify whether a journal is peer-reviewed?
There are several journal rankings, but I think your best bet is to look at the editorial boards/published works. Are they reputable researchers who are considered `pillars' of their respective fields? Are the papers that were published in that journal of general good quality, and relevant to your prospective submission?
Some red flags to look out for when deciding whether a journal has good practices:
- Journal is publicly listed on some blacklist (such as Bealle's list)
- Journal charges exorbitant fees for publication, and promises a fast turnaround time on publications.
- Journal emails you: good, reputable journals don't need to spam researchers for articles. That said, sometimes this is valid (say, you published in a CS conference that has a direct-to-journal track for fast publication turnaround, that is ok).
- Editors are relatively unknown people from non-research oriented universities
- The papers submitted there are garbage (not 'unclear' but absolutely unreadable/weird)
In general, research publications are about disseminating your ideas to a certain community. It's important to see where your community publishes, and go for these venues.