What are some of the central symbols in Death of a Salesman?
The Lomans' refrigerator is an important symbol of the shallowness of materialism. Willy bought the fridge on hire purchase, and though he still hasn't finished paying for it, it's stopped working properly. Much the same could be said of other consumer goods that he's bought, such as the washing machine and the vacuum cleaner. The Lomans are in over their head, mired in debt that they'll never be able to repay. The materialism of the consumer society holds out the promise of an easier life, one made more comfortable by labor-saving devices, but there's ultimately a heavy price to pay, a price not worth paying.
Stockings are also symbolically significant. Linda's stockings have holes in them so she starts trying to darn them. Willy's furious at this and orders her to throw them out; he'll buy her a new pair. Years ago, Willy had bought a pair of stockings as a gift for his mistress. Seeing Linda try to mend her stockings makes him feel incredibly guilty, reminding him as it does of his extramarital affair. It also offends his sense of manliness; he's the breadwinner of the family. In his own mind, he's a success, a "well-liked man." It's shameful for him to see his wife have to make do and mend.
The stocking symbol is important for another reason. When Willy sees Linda mending her stockings, it's an unwelcome intrusion of reality into the fantasy world he's constructed for himself. It's a brutal reminder that Willy's nowhere near as successful as he thinks he is. If he really were such a hot-shot salesman, then Linda wouldn't have to mend her stockings.
One of the most important symbols in this excellent tragedy is the seeds that Willy constantly refers to and which he tries to plant towards the end of the play. They symbolically represent Willy's need to have something that he can leave for his family, some kind of legacy, after his death. When he tries to grow some vegetables at night this symbolises his deep embarrassment about not bringing in enough of a salary to support his family, and that he will have nothing to leave his wife and children when he passes. Note what he says at the climax of Act II:
Nothing’s planted. I don’t have a thing in the ground.
Here Willy realises that he has nothing to show for his life and work, and that his death will end up in him being forgotten. It is also important to realise the way in which the setting plays an important part in Willy's inability to grow anything. The big buildings that crowd out the sky represent the American Dream and materialism that drive Willy to his premature grave. Miller is making the point that these actually make growing things, or trying to leave a legacy, often impossible.
At the same time, the seeds also represent his nurture of Biff. Willy recognises that his eldest son, once the apple of his eye and the repository of all of his hopes, is growing up to be nothing more than a "lazy bum" as Willy himself refers to him. This of course reflects on Willy's own failure to raise him to be successful.