The ordinary view is that the mind is an enduring structure that gives rise to, but is distinct from, the various events composing one’s stream of mental activity. Hume denied this, his positing being that there is the stream of mental activity, there being no underlying structure.
His position is false, because if a person goes into a coma or a cryogenic freeze and then wakes up, his mind wakes up with him, so to speak, showing that it was always there, notwithstanding the absence of activity.
Hume’s argument for his position is that, when he introspects, he does not encounter a self but only so many specific sensations and perceptions. But this proves nothing, since, when I look at a table, I don’t see molecules—even though that is what a table consists of.
As for why Hume countenanced this argument, it is because he was a strict empiricist and therefore denied the existence of anything for which there was not immediate observational data.