Watch one billiard ball strike another. You see motion, contact, and then more motion. You hear the click. But do you see necessity? Do you observe the must that supposedly ties the effect to the cause? Hume insists you do not. You see sequence; you never see compulsion. Repeat the experiment a thousand times: you get the same sequence, but you never get a glimpse of the supposed necessary bond.
Then where does our idea of necessary connection come from? From the mind itself, not from the world. After observing similar sequences repeatedly, the mind develops a habit: when A appears, it expects B. The felt compulsion — the sense that B must follow — is this habit of expectation projected onto the objects. Necessity is not in the world; it is in us.
Hume's official definition of cause becomes famously deflationary: cause is "an object followed by another, where, upon the appearance of the first, the mind is determined by custom to expect the second." That is all. There is no deeper metaphysical glue. The universe is a sequence of events; the necessity we read into it is a feature of our psychology, not of reality.
The analysis of necessary connection occupies Section VII — the longest and most technically dense section of the Enquiry. Hume regarded it as the centrepiece of his empiricist programme.