After her soliloquy, Malvolio enters. Olivia hands Malvolio a ring and tells him that Cesario left it as a gift or love-token from the Duke. Olivia orders Malvolio to chase after Cesario and return the ring to him.
However, Cesario actually left no such ring. The ring belongs to the Countess herself. She is just trying desperately to find a way to get Cesario to come back to her. She hopes that Cesario will return for an explanation.
Time and again Shakespeare reveals that love often causes one to act foolishly and irrationally. In the conflict of love vs. reason, love is the more powerful force. Olivia herself realizes that she is being irrational:
I do not know what, and fear to find
Mine eye too great a flatterer for my mind.
(278-79)
In these metaphorical lines, the eye refers to love (for love enters through the eyes) and the mind represents reason. The eye has flattered reason: the eye has convinced reason to be unreasonable and to feel love. Love is an emotion: it is an irrational entity that reason cannot control.
The first act ends with Olivia declaring that she cannot control herself or the situation. She is a victim of destiny:
Fate show thy force. Ourselves we do not owe.
(280)
The word owe here actually is poetical expression for own. Olivia is expressing the idea that people cannot own or control their own lives, their own destiny. Shakespeare frequently expresses the belief in Fate as an overwhelming and potent force in the universe that is beyond the control of any man or woman. People cannot control their feelings of love any more than they can control the time and place of their birth. Everyone is a victim to fate.