I know what it means, but the one I am responding to isn't, either out of ignorance or deliberately.
It doesn't mean anything more or anything less than that these people are verified to be who they claim they are. But the person above is trying to indicate it means some kind of "endorsement" by some vague "establishment" that he dislikes.
Blue checks typically mean large (sometimes rabid) twitter followings. Sometimes that’s fine but often their engagement in a topic can really derail it. Blue checks in practice mean more than just “verified account”.
Side note: anonymity can often improve the quality of online discussion. See: “breaking the social media prism”
