A miracle is a violation of the laws of nature — a departure from the uniform course of experience that grounds our most confident beliefs. The very reason we believe in laws of nature is the unbroken regularity of experience. A miracle, by definition, is an event against which the entire weight of human experience testifies.
The question is not whether miracles are logically impossible, but whether testimony for a miracle should ever outweigh the evidence against it. Hume's argument: a wise person proportions belief to evidence. The evidence for a law of nature is the strongest possible — uniform human experience. The evidence for a miraculous violation is, at best, the testimony of a few. The scales never balance.
Hume adds four reinforcing observations: miracle reports tend to come from ignorant and superstitious peoples; people have a powerful natural tendency to love the marvellous and to believe what excites them; all religious traditions produce miracles that cancel each other out; miracles cluster around periods of darkness rather than light. Each consideration further diminishes the probability of any given miracle claim.
Hume's argument has been challenged on many grounds — notably that it seems to assume what it sets out to prove by treating laws of nature as incapable of exception. But its central insight survives: the evidential burden on miracle claims is extremely high, precisely because the concept of a miracle is defined against the background of unbroken natural regularity.
Section X, "Of Miracles," was the passage Hume was most nervous about publishing. He reportedly circulated it privately for years before including it in the Enquiry. It was answered by numerous divines and remains the locus classicus of philosophical discussion of miracles.