A miracle may be accurately defined, a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent.
This is usually passed over without much comment, but the wording is significant, I think, since it seems carefully formulated in terms reminiscent of the dispute between Malebranche and Arnauld. Hume was certainly acquainted with at least the basic outlines of the dispute between the two -- when he had lived in France he had read all the French philosophy he could get his hands on, and the Malebranche-Arnauld dispute was one of the most significant philosophical events of the late seventeenth century. That dispute was enormously wide-ranging, but one of the major issues was how God's providence achieves particular effects.
Malebranche had argued, for essentially Trinitarian reasons, that God does all things according to Order, and thus by willing general laws and, what is more, those general laws that are most suitable to divine "simplicity of ways". As he says at one point (OC 3:215; LO 663), "God does not multiply his volitions without reason; He always acts in the simplest ways." This raised the question (and Arnauld raised it very vehemently) of how it is that God can work miracles, which seem to deviate from general laws and to introduce complexities into God's actions. Malebranche's response to this through time doesn't seem entirely consistent, but at one point he argued that God will on occasion engage in particular volitions, if by doing so He can more perfectly express His divine attributes. He insists (OC 8:661) that such particular volitions are very rare. Arnauld responds, at various poitns in the discussion, that this position either makes miracles impossible or is entirely arbitrary, making exceptions it cannot in principle allow.
However, Malebranche also has another account of miracles that shows up in other passages (e.g., the Dialogues) that miracles are actually not, in a proper sense, violations of divine laws, but simply the expression of higher-order laws given occasional causes. So in other words, he also has an account of miracles in which miracles are entirely regular events, but they are governed not by laws of nature but by some other kind of law (e.g., moral laws, or laws of grace); God wills these laws, which are still perfectly general; but they govern particular agents who do not always act. When a certain kind of agent (say, Adam in the state of original justice, an angel, or Jesus Christ) does a certain kind of thing, the law, so to speak, kicks in and, by force of the divine will (which establishes all laws of cause and effect), the miraculous effect follows. In such a case the agent in question is an occasional cause of the miracle, the occasion on which God's efficacy in willing a law makes the effect to happen.
All the above is fairly crude as a summary of a complicated set of discussions, but it gives the basic gist of the positions. We find in Malebranche, then, the materials for two distinct accounts of miracles: a particularist account, in which God directly wills a particular exception to general law by a 'particular volition'; and an occasionalist account, in which God wills a general law that, on particular occasions, results in the miraculous effect. It can hardly be coincidence that both of these show up in Hume's 'accurate definition'. On both accounts, miracles are violations of laws of nature. (On the occasionalist account, miracles are themselves results of laws, of course, but they are the results of laws higher and more closely connected to the divine ends than the laws of nature.) Hume's definition seems to be carefully formulated to allow for both particularist and occasionalist accounts of miracles; both are found in Malebranche; and Hume was an extensive reader of Malebranche.
I'm not sure how this affects the overall interpretation of the essay; but it is an interesting link between Hume's essay and prior discussions of miracles.
