The conclusion Hume reaches, then, is that we can perceive only constant conjunction between two events, and not necessary connection. Constant conjunction, to reiterate, is simply the observation that two events seem to go together quite frequently. Necessary connection is the perception of some connection between the two events that explains why they go together. While Hume undercuts any rational basis for believing in necessary connection, he suggests that the mind projects the idea of necessary connection onto events that it observes to be constantly conjoined. Our notion of causation is then not the combination of constant conjunction and necessary connection, but rather the combination of constant conjunction and the determination of thought that conjures up the idea of necessary connection.
Part 2 rescues us from the extreme skepticism of Part 1 by suggesting that there is a way in which talk of necessary connection and causation can be meaningful. Hume remains skeptical to the extent that he does not believe in a necessary connection that outstrips constant conjunction. While he concludes that we can speak meaningfully about causation and necessary connection, these terms have been limited to the extent that they now bear no more metaphysical weight than talk about constant conjunction. To talk about causes or necessary connections is no more than to talk about the combination of constant conjunction and a determination in our thoughts. As a result, it is not clear how we can meaningfully speak about a metaphysical connection between two events that goes beyond their constant conjunction and the belief that there is some necessary connection.
We might want to say "yes, I may not perceive the necessary connection between a flame and its power to burn, but there is something more than simply a constant conjunction between the flame and the burning." Hume's argument is that there is no intelligible way to talk about that "something." We cannot call it a cause, since he has reduced the term "cause" to being a combination of constant conjunction and a determination of thought. If all our terms must be reducible to simple impressions, and if there is no simple impression of that "something" which connects cause and effect, then there is no intelligible way to talk about cause and effect that goes beyond Hume's somewhat unsatisfying limitations.