This quote comes in the first scene when Petruchio starts to woo Katherine in Act II scene 1. What is amusing about this scene is that Petruchio plays the role of the traditional lover, only to comment on and satirise his words. Thus it is that he compares Katharina in the quote you have identified to Diana, the Roman goddess of the hunt and of chastity. Note the full comparison:
Did ever Dian so become a grove
As Kate this chamber with her princely gait?
O, be thou Dian, and let her be Kate,
And then let Kate be chaste and Dian sportful!
Katherina's typical response to such a flattering and obsequious comparison is to ask where Petruchio "studied" such "goodly speech," and Petruchio's reply again draws attention to the ridiculous nature of his wooing. Petruchio in this quote therefore starts off by saying that Kate has made the chamber beautiful with her presence, just as Diana, the goddess, makes woodland groves divine with her presence. The second part of the quote implores Kate and Diana to swap places so that Kate can be "chaste" and the new Diana before him can be "sportful," which is richly suggestive and rather ironic given the lack of success that Petruchio's artificial wooing has had so far. Thus the comparison of Kate to Diana is ironically used by Petruchio as part of his wooing.