The significance of Act III, scene I is the fate awaiting Oliver for all the wicked deeds he has done to his younger brother, Orlando. Moreover, this scene is a brief one and acts as a turning point through the tyrannous Duke Frederick who sends Oliver to the Forest of Arden in search of his younger brother. This scene can also be taken as the meeting of two villains of the story.
Plot in a gist:
The Duke enquires Oliver the whereabouts of his missing daughter Celia (who went missing along with Orlando, Rosalind and Touchstone) and wants Orlando back to him within a year’s time dead or alive. In case of his failing to bring back his brother, the Duke warns him that he would confiscate all his properties. When Oliver states that he loved his brother and that he has no intention to save him, the Duke again accuses him as “More villain thou” and calls his guard to take him out. After this incident Oliver goes to the Forest of Arden in search of his brother. This indeed paves the way for the principle of repentance and reconciliation of Oliver with his sibling in the further movement of the play.