In this poem's strange, disorienting first line, the speaker claims to have fallen "into the State" from his "mother's sleep." As that capitalization suggests, the speaker uses "the State" as a metonym for the government. This invites readers to imagine a government that has great power over the speaker—that controls the speaker, forces the speaker to act as the government wants, and doesn't much care about the speaker in return. After all, he doesn't choose to enter "the State," but helplessly falls into it, as if it were inevitable that he would eventually find himself at its mercy.
Although it's clear that "the State" is the speaker's way of referring to the government, the phrase "my mother's sleep" is more mysterious. The most literal interpretation is that the speaker slips from his mother's protection while she isn't paying attention—that is, while she's sleeping. But as the poem goes on, another possibility emerges: that the phrase "my mother's sleep" refers to the peaceful and safe environment of his mother's womb, implying that the speaker is a baby who goes directly from infancy to the harsh care of the government.
Because "The Death of the Ball Turret Gunner" gets pretty abstract and metaphorical, it's worth keeping its simplest meaning in mind. On its most basic level, this poem is about the speaker's experience of active combat in World War II, curled inside a ball turret, a compartment attached to the underside of a bomber plane. A soldier would crouch inside the ball turret (in a position similar to a baby crouched in its mother's womb), shooting machine guns to protect the plane from enemy fire. Although it doesn't become clear until later in the poem that the speaker finds himself in a turret, the title—"The Death of the Ball Turret Gunner"—prepares readers for this fact, and it helps to keep this context in mind when considering the poem's more complex moments. The poem, then, connects the baby in the womb to the man in the ball turret, and uses that juxtaposition to highlight the absurdity and horror of a man forced by his country to go to war.
The speaker's language in this opening line uses an intense sequence of repeated sounds, starting with the consonant /m/: "From my mother's sleep I fell into the State." This /m/ sound is particularly noticeable because the phrase "my mother's" is also alliterative, giving the opening words of the poem a rhythmic bump. Then the consonant /l/ sound in "sleep" and "fell" and the sibilant /s/ sound in "sleep" and "State" come in. All together, these repetitions make this first line feel startling, vivid, and intense—just as intense as finding oneself falling without warning out of one's mother's protection and "into the State."