Polonius, of course, does give Reynaldo the task of spying. This act fits nicely into the plot since it shows the distrust that the older generation has for the younger one. Notice how well it echoes Claudius's suspicions of Hamlet, and his later hiring Rosencrantz and Guildenstern to spy on Hamlet. In Act 1, readers may see Polonius as a contrast to the conniving, manipulative Claudius. But in Act 2, we see Polonius more like Claudius. Unlike Claudius, though, Polonius is just being nosy, maybe a little like parents snooping around on their sons' and daughters' Facebook accounts to find out what all they are doing in college. This scene sets up the motif of spying which occurs throughout the play, and makes the reader question the wisdom and integrity of the older characters and their relationships with their children.
This scene in Shakespeare's Hamlet can be interpreted as another scene in which Polonious is revealed to be inept, foolish, and long-winded. He has barely finished telling Laertes "to thine own self be true," (I:3) and here he is sending Reynaldo to spy on him (II:1). He takes too long to say what needs to be said, and then repeats it in a slightly different form.
By the way, Polonius gives Reynaldo money and letters for Laertes. Again, though, the main purpose of the meeting seems to be to give Polonius an opportunity to instruct Reynaldo on how to best get to know other Danes that can give him information on Laertes, which Reynaldo can then report back to Polonius.
The character of Reynaldo shows up in Act II, Scene 1.
In that scene, Polonius asks Reynaldo to go to Paris. While he is there, his job is going to be to spy on Laertes, the son of Polonius.
Polonius wants Reynaldo to spy on Laertes because he is not sure Laertes will behave himself in Paris.
Polonius does not have a really good reason to suspect Laertes of anything. But he sends Reynaldo to be his spy anyway -- I think he's sort of being overprotective or maybe excessively suspicious of his son.