A cautious Penelope, sought after by many clever suitors, uses the bed that she and Odysseus shared for so many years to trick Odysseus into proving his identity. The bed, carved from a tree that has its roots in the foundation of the house itself, is immovable, much like Odysseus and Penelope's loyalty to each other. Only Odysseus knows that it can't be moved without destroying it, and so Penelope knows that when she tells him she's had the bed moved, the only man who would be outraged by this confession is her true husband, the one who built the bed himself and kept the secret. Odysseus's anger is confirmation. Thus their marriage bed is not only a staple of the plot, but also a symbol of their enduring relationship, which has been strong enough to survive a separation of more than twenty years.
In Penelope's hands, the bed also helps reveal the qualities that she and Odysseus both share, and which have perhaps made their marriage such an unusually successful one (a rarity among Greek heroes—just look at how relationships worked out for Paris, Heracles, and Achilles). Both husband and wife share a propensity toward cleverness that is particularly unusual in the story. Odysseus is one of the few Greek heroes to epitomize brains over brawn. Even more remarkable is Penelope, whose womanly craftiness is most unusually accompanied by great virtue and purity instead of moral or sexual corruption.
The bed also represents the equality between husband and wife, similarly unusual in Classical literature; Odysseus tests Penelope many times before he is willing to believe that she has remained faithful and not encouraged (or secretly accepted) any of the suitors who plague her. With the bed, Penelope shows herself Odysseus's equal—she won't simply believe he is who he says he is! She wants to test him, too, and will do so before she accepts him.