The three caskets that suitors must choose from in order to win Portia's hand are gold, silver and lead. Each suitor chooses a casket based on the box and his understanding of the riddle presented with it. Each suitor deliberates about which casket to choose based upon his logical reasoning skills derived from his upbringing. Unbeknownst to Portia, her father's reasoning is what protects her from suitors who would not do well being her husband. For example, the African man from Morocco has nothing in common with Christian Europeans; therefore, his reasoning is based on what he perceives them to be. Morocco reasons not to choose the lead box because Portia is worth more than that; he believes that the silver box promises that he will get what he deserves, but that might not extend to Portia; and finally, the gold box represents her value and what many men seek. Hence, the Moroccan chooses the gold box and is told "All that glitters is not gold" (II.viii.65) and Portia is saved from being married to someone who does not understand her religion or her culture.
The Prince of Aragon (a pun on arrogance) displays his own conceited personality because he believes he is better than the "many" who would choose the gold box. He doesn't choose the lead box because it is not beautiful enough even to consider. Therefore, he chooses the silver casket because its riddle says that he shall get what he deserves--and he feels he deserves everything and anything he wants. Since he chooses incorrectly, Portia is saved from having to marry someone who is arrogant and self-serving.
Bassanio, on the other hand, presents himself as the humble Christian that Portia's father would have wanted her to marry--even if he is poor. His logic stems from his common upbringing which values the spiritual over the temporal. Bassanio looks upon the gold and silver caskets as possible temptations or deceivers. They may look good and be desired by the world, but they cannot buy what matters most in life. He draws an analogy to beauty products cover up hair and faces (wigs and makeup) but the truth is revealed once those things are taken away. The lead box, however, offers no deceit and stands for itself without disguise. Bassanio reasons as follows:
"But thou, thou meagre lead,
Which rather threaten'st than dost promise aught,
Thy paleness moves me more than eloquence
And here choose I. Joy be the consequence!" (III.ii.104-107).
Bassanio chooses lead because it does not promise anything beyond itself. It doesn't boast or brag and it doesn't tempt or disguise itself. He concludes that Portia's picture must be in a casket that represents truth rather than great speeches or beautiful things of the world might offer.