What metaphilosophical naturalism means

Metaphilosophical naturalism = scientism = verificationism.

Here are some of the best statements of naturalism I have ever read in the philosophical literature:

"there is no such as a justifiable purely philosophical conclusion about any empirical phenomenon (and there are no such things as "non-empirical phenomena"). Therefore, anyone who wants to defend a philosophical thesis had better be prepared to defend it as, in large part, a scientific proposition based on scientific evidence. ... one should try to make the science in question independently interesting as science, even (indeed, escpecially) to people whose tastes don't run to philosophy." (Don Ross et al: Midbrain Mutiny, 2008)

"It is the mission of scientific institutions to strive to provide a complete objective account of the universe at all scales of description. This ambition can never be realized, but that is only because scientists will never be able to make every possible observation or take every possible measurement - not because there is a rival path to knowledge, such as religion or intuitive insight, that performs better in some domains of inquiry." (Don Ross: Philosophy of Economics, 2014)

"Since science just is our set of institutional error filters for the job of discovering the objective character of the world - that and no more but also that and no less - science respects no domain restrictions and will admit no epistemological rivals (such as natural theology or purely speculative metaphysics). With respect to anything that is a putative fact about the world, scientific institutional processes are absolutely and exclusively authoritative.

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no hypothesis that the approximately consensual current scientific picture declares to be beyond our capacity to investigate should be taken seriously.

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naturalism and verificationism are the same thesis, or almost the same thesis." (James Ladyman and Don Ross: Every Thing Must Go: Metaphysics Naturalized, 2007)

They are of course talking about epistemic, not semantic, verificationism. The hypotheses of analytic metaphysics are meaningful. They are just not worth investigating.
Ladyman and Ross don't say this, but a direct consequence of epistemic verificationism is that most debates that are currently going on in philosophy (i.e. Humeanism vs non-Humeanism about laws of nature) should be abandoned completely. They are not resolvable by ordinary scientific/empirical/mathematical means, and are therefore a waste of time. This is also my opinion. If you can't figure out a way to solve your question empirically or mathematically, you should abandon it, and stop wasting your funders' money.