The movie let's audiences draw their own conclusions, but Clarke's novelization is more concrete. In the book, the Monolith sees the potential in the early bipeds and decides to give a little "push", tweaking neurons and fiddling with some gene strands. A couple of the man-apes drop dead from the editing.
As for the Monolith on, or rather a bit under, the Moon, that was effectively a test for the Humans. If they had to capability to dig out the slab, it would then send a signal to the outer gas planets (Jupiter in the film, Saturn in the original novel and Jupiter in both the novel and the movie "2010"), informing the Stargate capable Monolith that humans were ready to "meet the makers" (provided Humans decide to follow the signal).
One potential flaw with the Lunar test, in my probably flawed opinion, the Monolith could have been accidentally exposed by a natural asteroid strike without the direct interactions by humans. In Clarke's original short story that inspired the movie and novel, the artifact (I think was a pyramid or tetrahedron) was surrounded by a "field" that could only be disrupted by a nuclear induced detonation, something less likely to occur through natural causes. Like the film and full length novel, once exposed, the object transmits a signal...and the story ends with humans wondering, "Uh, I think we just signaled the creators! What do we do?"