1 It could mean to solve every problem recognised or recognisable as metaphysical. The idea of metaphysics here meaning the most fundamental and pervasive features of reality - causation, change, identity, essence, existence, possibility, necessity, universal and particular, the mind/ body distinction or whatever list another philosopher prefers.
2.It would mean to remove the root of metaphysics, the attitude and ways of thinking about thngs that sees certain problems as metaphysical. There is more than a hint of this in the later work of Wittgenstein, Philosophical Investigations (1953). Wittgenstein had the idea that problems we regard as metaphysical are the result of the misuse or misunderstanding of language : 'Philosophy is a battle against the bewitchment of our intelligence by means of our language'(PI,§109).
To create an example : we (or some folk) talk of the mind/ body problem as if the mind were a thing like the body in the sense that it is a continuing object about which statements can be made and which can have certain features. X has a sharp mind just as Y has a fit body. We treat 'mind' as a noun just as 'body' is a noun.
But while 'body' does indeed refer to a continuing object, persisting at least through a period of time, 'mind' doesn't refer to an object at all. To talk of someone's mind is to talk of a set of capacities and dispositions which that person has - to calculate, to imagine, to infer, to suspect or expect, to work out means towards ends and apply rules of cases. To say that X has a sharp mind is not to say that there is some object that constitutes X's mind and is sharp; it is just to say that X can take in information quickly, can make accurate deductions, can suggest how to deal effectively with problems.
Point is, if Wittgenstein is right then the mind/ body problem is bogus, a product of the misleading use of language. Plenty of people will disagree with this; and I am only setting out a quick sketch of a contentious position. But can you see that on Wittgenstein's approach it might be possible, by a logically clear view of language, to remove the metaphysical impulse - and 'solve' metaphysics by dissolving it.
Press questions if I haven't put things across clearly enough. The implications for society take us into sociology and might be better addressed on another site of the Stack Exchange.
[Apologies to Wittgensteinian scholars. This is meant only to give a rough first view - all that's possible here - of the kind of approach with which Wittgenstein was associated.]