What are the elysian fields?

The Elysian Fields are a mythological place where ancient Greeks believed the souls of the deceased heroic and virtuous people went to rest. It is similar to Paradise in monotheist beliefs.

It is the "heaven" of sorts that the poets, priests, and the higher-than-average people would go when they died. So it is a part of Hades, the underworld.

Ee-lay-gen

In A Streetcar Named Desire, Elysian Fields is the name of the street upon which Stanley and Eunice's apartment is located.

It's the street that Stella and Stanley Kowalski live on.