Once we had a country and we thought it fair,
Look in the atlas and you'll find it there:
We cannot go there now, my dear, we cannot go there now.
This moment in the poem is one of several emphasizing the disconnect between the written, officially sanctioned version of the world and the material reality in which the speaker lives. While the speaker's home country (later revealed to be Germany) still exists on the map, it may as well not exist from the speaker's point of view, since they cannot set foot inside its borders. This line also sets some basic storytelling conditions for the rest of the poem. It's important from a storytelling perspective that the speaker be able to complain about mistreatment as a refugee without readers wondering why they don't simply go home. This part of the text neatly prevents that from happening, since the speaker unequivocally states that there is no way they can return.
Came to a public meeting; the speaker got up and said;
"If we let them in, they will steal our daily bread":
He was talking of you and me, my dear, he was talking of you and me.
This part of the poem addresses and critiques the scapegoating of refugees. At several points in the text, most explicitly here, the speaker seems to marvel at how much others feel threatened by refugees or Jews—even when, as the speaker's words make clear, they aren't in a position to cause harm. In fact, the version of refugees conjured by the person speaking at the public meeting is completely imaginary, with little to do with real refugees. Moreover, this quote hints that Nazi fearmongering about Jews is actually not so different from fearmongering about refugees elsewhere. Both imagine a relatively powerless group of people to be very sinister and capable of harming others.
Walked through a wood, saw the birds in the trees;
They had no politicians and sang at their ease:
They weren't the human race, my dear, they weren't the human race.
Here, the speaker expresses clear envy for the birds living without the burden of political oppression or borders. The stanza's final line, however, can be interpreted in two rather contradictory ways. Its more immediately striking tone is one of resignation and even despair. Animals, the speaker suggests, are able to live "at their ease" because they are, simply, animals—therefore it's not helpful for humans even to hope to be like them, since they can't change the most fundamental difference between themselves and the animals around them. At the same time, the line suggests that human-made problems like war and borders are exactly that: human-made. If humans are anomalous within nature, this means that they may be able to redeem themselves and become more like, or at least live in proximity to, the happier animals around them.