In Shakespeare's Hamlet, what had the players come to do?

In Shakespeare's Hamlet, the players
come to Elsinore to do what they do, put on plays.  They are a traveling group of
actors.  They are entertainers.  In short, that is the answer to your
question.

In terms of the drama, they serve the function of
presenting the "play-within-the-play," which not only draws attention to the theme of
acting/pretending/seeming in the play, but also draws attention, after a bit of
manipulation by Hamlet, to Claudius's guilt as the murderer of King Hamlet.  Claudius's
reaction to the murder scene that presents a murder similar to that he committed,
convinces Hamlet that Claudius is, indeed, guilty of murdering his
father.

The players also provide opportunities for Hamlet
to ruminate on acting theory, and serve as catalyst for Hamlet's "Hecuba"
soliloquy.

Again, though, in short, the players come to put
on plays.