Meet is the greatest common refinement of two Judgements — what two Judgements share at their most specific.
Given two Judgements, there may be many Judgements that both subsume. The Meet of two Judgements is the most specific such shared Judgement — the one that captures everything the two have in common and nothing more. It is the “and” of Judgements: to satisfy the Meet of A and B is to satisfy both A and B.
Meet is forced by Order. If Judgements can be compared by subsumption, then the question “what do these two agree on?” must have a determinate answer. Without Meet, Order would be incomplete — there would be pairs of Judgements with no way to express their common ground.
Together with Join, Meet forces Implication.