The hints Portia gives to help Bassanio choose the right casket all have to do with the same theme - the importance of looking beneath the surface to find what is important. At the beginning of Act III, Scene 2, Portia says to Bassanio,
"Beshrew your eyes, they have o'erlooked me" (lines 14-15).
The accepted meaning of these words indicate that Bassanio has bewitched Portia with his eyes, but a second meaning hints that in using his eyes to find Portia, Bassanio is missing her, the part of her that is important. A short time later, Portia, referring to the caskets, says to Bassanio,
"I am locked in one of them. If you do love me, you will find me out" (lines 40-41).
Portia here, in talking about love, is saying that if Bassanio looks at the caskets with the eyes of love, he will look beyond their surface appearances to find what is underneath, the essence of the entity, which is to what true love is drawn.
When Bassanio begins his rumination of the caskets, Portia sings softly in the background,
"Tell me where is fancy bred,
Or in the heart or in the head?...
It is engendered in the eyes
With gazing fed, and fancy dies" (lines 63-64, 67-68).
In these lines, Portia is saying that when the eyes are done gazing, fancy dies. What attracts the eyes is impermanent and, in the end, inconsequential; when Bassanio hears these words, he begins to think along the lines that Portia wants him to think, musing,
"So may the outward shows be least themselves;
The world is still deceived with ornament" (lines 73-74).
Guided by Portia's subtle hints, Bassanio eschews the showy, prettily decorated caskets and chooses the plain, lead one, which is the one that wins him Portia's hand.