The whole of book 21 revolves around Odysseus's bow.  This alone shows how important this object is.  It represents so much about Odysseus--his power, skills, intelligence, etc.  This bow shows that no one could take Odysseus's place.  First Penelope presents the challenge that whoever can hit 12 axes in a row with it she will then marry, and none of the suitors can complete the task.  This shows that none of them can have Penelope like Odysseus can.  It also shows that they will never hold his position or have the kind of power that Odysseus does.  She also asks the men to string the bow, and no one can do that either.  This shows that none of the men are as skilled, strong, or intelligent as Odysseus.  As a whole, the bow symbolizes Odysseus.  He is one of a kind and cannot be beat.

The bed obviously represents Odysseus's and Penelope's marriage.  Odysseus built it himself with great craftsmanship and skill.  He carved it out of a tree, bolted it down, and ornately decorated it.  This is like his and Penelope's marriage.  It was sturdily built, held down/together with trust and love all the years Odysseus was away, and it was showered with good memories and great wealth.  The fact that it cannot be moved represents how strong their bond and marriage in general is.  All the years that Odysseus was away never actually tore them apart.  They were always "faithful" to each other, knowing that they would one day be reunited.  They struggled, but they were always married and always would be.  The bed would not be moved or undone, like their marriage.