What is the significance of plant, tree, and seed imagery in Death of a Salesman?

The plant, tree, and seed imagry all refer to growth, or at least the potential for growth.  When Willie was younger, he was able to plant a garden and make things grow ... clearly there was the implication that Willie was creative and hoped to "grow" as well.  Later on in the book we find that Willie's house has been surrounded  by tall apartment buildings that block out all the sun and make it impossible to grow anything.  

In Act II, part 6, after Willie's final disappointing dinner with his "boys," we find that he has bought some more seeds and is trying again to "grow" something.  Ben appears and speaks to him, telling him it is a cowardly solution, but that his insurance would provide a significant amount of money for his family, especially Linda.  We know that the flowers/vegetables won't grow, and we also know that his insurance plan won't "grow" either. But, as with many other things in his life, Willie decides to go it on his own.

The greatest irony is that they don't need the money; Linda remarks that she made the final payment on the house the day of Willie's funeral.  "We're free,"she remarks ... but Willie isn't there to share the freedom.  Once again, Willie tries to "grow" something, but it isn't going to happen ....

What do the seeds symbolize in Death of a Salesman and why is their planting significant?

The seeds in Death of a Salesman have a dual significance. Taken literally, they represent seeds, as Willy says, to plant and grow a garden. Willy wants to grow carrots, peas, beets and lettuce in his backyard. The significance of these particular seeds is that they will give rise to vegetables, as opposed to flowers or other non-edible plants. Metaphorically, Willy wants to nurture his family by cultivating a garden.

The seeds are also meant to show that perhaps Willy and Biff are not so different after all. Biff realizes that he is not cut out for office work or for the life of a traveling salesman. Willy never acknowledges it to himself or to his family, but he might have been better off working in another capacity rather than as a traveling salesman. He blames his failures on others, noting that if the boss's father were still controlling the company, Willy would have risen to a much higher level. This seems unlikely. More likely is that Willy never stood out as particularly adept. He might have had greater success and happiness had he recognized that he enjoys planting and working with his hands, as Biff realizes about himself.

The seeds also symbolizes creating something of permanence to leave behind. The seeds metaphorically are also Willy’s children and he wants to do a better job with them than he has with Biff. The juxtaposition of the planting scene and Biff’s announcing that he is leaving and will not return is not a coincidence. Willy has failed with his firstborn seed, Biff, and compulsively needs to plant a garden with other seeds. The discussion about the seeds is sandwiched between Linda’s mention of how handsome Biff looks in his blue suit and Biff “taking the hoe from Willy” and saying good-bye.

Just as Willy failed with his paternal planting, Linda laughingly—because she does not recognize the dual significance of the seeds—tells him that the backyard does not get enough sun and “nothing’ll grow anymore.”