The poem's first three lines capture the speaker’s anxious, fretful state of mind. Sometimes the speaker is so full of sorrow and anxiety that even the slightest sound can wake them up at night. They're totally on edge thinking about how life will turn out for both them and their children.
The “fear” the speaker talks about in these lines isn’t anything specific, but a kind of general worry about what is going to happen in the future. Given the poem’s focus on ecology and nature, the “despair” that the speaker feels could relate to the future of the planet itself. Or, considering this poem was written around the time of the Vietnam War and the Cold War, perhaps the speaker worries about humankind destroying itself.
Keeping things general, though, gives the poem a universal feel. The lack of specifics is part of the poem’s power: most people can relate to that visiting sense of dread when the mind runs away with itself during the small hours.
Of course, this all starts with a "When"—when the speaker feels these things, something happens. The speaker delays that something for these three lines, however, which evokes the sense of mounting anxiety. The deliberate delay of the response to that "When" creates tension, the reader searching for grammatical relief that takes a long time to come.
Enjambment contributes to this sense of restlessness too, the speaker's thoughts seeming to run away with themselves across multiple lines. Line 3 also uses subtle repetition, highlighted below:
in fear of what my life and my children’s lives may be,
The repetition of “my” and “life/lives” (the latter being polyptoton) make the line feel jumpy and pained, evoking the way an anxious mind cycles repeatedly through patterns of thought. If the speaker’s not worrying about their own life, they're worrying about their children’s future, or that of the entire world—and these worries keep coming back during the night, bubbling up from the subconscious mind and waking the speaker up.