The metaphor in the first stanza compares a life with no dreams to an incapacitated bird: the speaker says

For if dreams die
Life is a broken-winged bird
That cannot fly (2–4).

A metaphor is a comparison of two unalike things in which one is said to be the other. Here, a life without dreams is likened to a bird that can no longer do the thing that we typically think of birds as doing: flying. This bird is damaged, with a broken wing, and so it cannot fly: how would it migrate? How would it get to its nest, its home? The short answer is that it couldn't. It would not be able to do any of the things that a bird who depends on its ability to fly normally does. This metaphor creates a rather pathetic image and a sorrowful mood, as it seems as though such a bird would, inevitably, die. At the very least, its life would be rather empty. What this means for life is that a life without dreams is as unlivable and as terribly sad as the broken bird's; a person cannot do what people are meant to do. This suggests that our ability to dream is as central to our experience as flight is to a bird's. We cannot be our complete selves if we have no dreams.